Digit substitutions by ‘+’
and ‘=’ signs
(inside an integer)
[January
26th, 2009]
Hello Math-fun,
... stupid idea,
yesterday, to get asleep:
Let's examine a 5-digit integer like abcde; if we decide that b is the + sign and d the = sign,
we have the simple equation a+c=e.
This equation has a lot of solutions (like
1+2=3 or 1+0=1)... but once we have decided that (for instance) 4 is coding
"+" and 8 is coding "=", we cannot use elsewhere (in the
integer) the digits 4 and 8.
Thus, with the [4+;8=]
convention, a valid 5-digit integer would be, for instance, 14283. Or 14081. Or 18041 (1=0+1). But not
24284 (2+2=+). Neither 04585 (no leading zero).
Questions:
a) What is the best [x+;y=] coding in order to produce the biggest quantity
of valid 5-digit integers?
b) Same question for a 6-digit integer?
c) Same question for a 7-digit integer? (where 1424386 --> 1+2+3=6 would now be valid too!)
Best,
É.
(now asleep)
---
Hans
H. kindly asked me to be more precise in defining a sound “equation”; we started
the following dialog:
[HANS] :
Is there anything else in
the following 154 "solutions" that should be excluded?
1) 10=10 2) 11=11
3) 12=12 4) 13=13 5) 1+0=1
6) 1+1=2
7) 1+2=3 8) 1+5=6
9) 1+6=7 10) 15=15 11) 16=16
12) 17=17
13) 1=001 14) 1=0+1 15) 1=1+0
16) 1=1=1 17) 1=+01 18) 19=19
19) 20=20 20) 21=21 21) 22=22
22) 23=23 23) 2+0=2 24) 2+1=3
25) 2+3=5 26) 2+5=7 27) 2+7=9
28) 25=25 29) 26=26 30) 27=27
31) 2=002 32) 2=0+2 33) 2=1+1
34) 2=2+0 35) 2=2=2 36) 2=+02
37) 29=29 38) 30=30 39) 31=31
40) 32=32 41) 33=33 42) 3+0=3
43) 3+2=5 44) 3+3=6 45) 3+6=9
46) 35=35 47) 36=36 48) 37=37
49) 3=003 50) 3=0+3 51) 3=1+2
52) 3=2+1 53) 3=3+0 54) 3=3=3
55) 3=+03 56) 39=39 57) +00=0 58) +01=1 59) +02=2
60) +03=3
(...)
[ERIC] :
Hello Hans,
... gee,
how fast !
> 13) 1=001
> 17) 1=+01
> 57) +00=0
> 58) +01=1
... those
look awful, don't they?
[HANS] :
Could you be a little more explicit about
what "true" statements look awful?
[ERIC] :
... ouch, this is
not easy for me, as I'm not a pro
mathematician but only an amateur... Let me see...
Some vocabulary,first:
--> k-digit
integer:
an integer written with k concatenated digits (example:
12045 is a 5-digit integer; k=5, here).
--> Substitution:
we note [x+;y=] the substitution
of the digit "x" by the symbol "+" inside the k-digit
integer and the substitution of the digit "y" by the symbol
"=" inside the same k-digit integer. Those substitutions occur
simultaneously (example: [4+;8=] asks to replace,
inside the k-digit integer, every "4" by a "+" sign and
every "8" by a "=" sign. The 5-digit integer 12489
produces, in this example, the string of characters 12+=9).
--> Equation:
the k-digit integer, after [x+;y=],
becomes a string of symbols which must be seen as a "classical
equation".
--> Classical
equation:
an egality where something placed
to the left of the sign "=" is arithmetically equal to what is placed
on the right of the same "=" sign (examples: 1+3=2+2 or 1+0=1 or
22=22).
--> Gertrude
Stein notation (“a rose is a rose is a rose”):
we accept strings with more than one "=" sign, but
the resulting equation, though not being "classical", must still say
the truth (1=1=1 is valid, 7=5+2=1+6, 9=4+5=9 are valid too)
--> Quantity:
what is placed next to a "+" or next to an
"=" sign
Rules.
Before the substitution:
The first digit of a k-digit integer
cannot be zero (01234 is forbidden)
After the substitution:
a) no
two "+" signs may follow each other; no two "=" signs
either.
b) two
substrings are forbidden: "+=" and "=+"
c) no
"+" or "=" can start or end a string
d) no
quantity can have a leading zero
e) the equation must be true
[HANS] :
(...)
We've already decided that the initial
digit should not be "0". Let's add the proviso that the initial TWO
digits should not be "+0". In addition, let us disallow ANY of the
following substrings: {"++", "+00", "+01",
"+02", "+03", "+04", "+05",
"+06", "+07", "+08", "+09",
"=00", "=01", "=02", "=03",
"=04", "=05", "=06", "=07",
"=08", "=09", "=+0"}. There might be other things
we won't like, but let's see what we get so far...
Number
of 5-digit solutions:
=\+
0 1 2
3 4 5
6 7 8
1 114
2 116
104
3 118
108 110
4 120
110 110 114
5 120
110 112 114
116
6 122
112 114 114 114 114
7 124
114 116 114
116 116 118
8 126
116 114
116 116 118
120 122
9 128
114 116 118
120 120 122
124 126
Maximum
(128):
1 1+1=2
2 1+2=3
3 1+3=4
4 1+4=5
5 1+5=6
6 1+6=7
7 1+7=8
8 11=11
9 12=12
10 13=13
11 14=14
12 15=15
13 16=16
14 17=17
15 18=18
16 1=1=1
17 2+1=3
18 2+2=4
19 2+3=5
20 2+4=6
21 2+5=7
22 2+6=8
23 21=21
24 22=22
25 23=23
26 24=24
27 25=25
28 26=26
29 27=27
30 28=28
31 2=1+1
32 2=2=2
33 3+1=4
34 3+2=5
35 3+3=6
36 3+4=7
37 3+5=8
38 31=31
39 32=32
40 33=33
41 34=34
42 35=35
43 36=36
44 37=37
45 38=38
46 3=1+2
47 3=2+1
48 3=3=3
49 4+1=5
50 4+2=6
51 4+3=7
52 4+4=8
53 41=41
54 42=42
55 43=43
56 44=44
57 45=45
58 46=46
59 47=47
60 48=48
61 4=1+3
62 4=2+2
63 4=3+1
64 4=4=4
65 5+1=6
66 5+2=7
67 5+3=8
68 51=51
69 52=52
70 53=53
71 54=54
72 55=55
73 56=56
74 57=57
75 58=58
76 5=1+4
77 5=2+3
78 5=3+2
79 5=4+1
80 5=5=5
81 6+1=7
82 6+2=8
83 61=61
84 62=62
85 63=63
86 64=64
87 65=65
88 66=66
89 67=67
90 68=68
91 6=1+5
92 6=2+4
93 6=3+3
94 6=4+2
95 6=5+1
96 6=6=6
97 7+1=8
98 71=71
99 72=72
100
73=73
101
74=74
102
75=75
103
76=76
104
77=77
105
78=78
106
7=1+6
107
7=2+5
108
7=3+4
109
7=4+3
110
7=5+2
111
7=6+1
112 7=7=7
113
81=81
114
82=82
115
83=83
116
84=84
117
85=85
118
86=86
119
87=87
120
88=88
121
8=1+7
122
8=2+6
123
8=3+5
124
8=4+4
125
8=5+3
126
8=6+2
127
8=7+1
128
8=8=8
This
gives the longest finite sequence of 5-digit integers, the code [0=9+] producing
a maximum of 128 terms:
S(5) =
10101, 11011, 12012, 13013, 14014, 15015, 16016, 17017, 18018, 19102, 19203,
19304, 19405, 19506, 19607, 19708, 20191, 20202, 21021, 22022, 23023, 24024,
25025, 26026, 27027, 28028, 29103, 29204, 29305, 29406, 29507, 29608, 30192,
30291, 30303, 31031, 32032, 33033, 34034, 35035, 36036, 37037, 38038, 39104,
39205, 39306, 39407, 39508, 40193, 40292, 40391, 40404, 41041, 42042, 43043,
44044, 45045, 46046, 47047, 48048, 49105, 49206, 49307, 49408, 50194, 50293,
50392, 50491, 50505, 51051, 52052, 53053, 54054, 55055, 56056, 57057, 58058,
59106, 59207, 59308, 60195, 60294, 60393, 60492, 60591, 60606, 61061, 62062,
63063, 64064, 65065, 66066, 67067, 68068, 69107, 69208, 70196, 70295, 70394,
70493, 70592, 70691, 70707, 71071, 72072, 73073, 74074, 75075, 76076, 77077,
78078, 79108, 80197, 80296, 80395, 80494, 80593, 80692, 80791, 80808, 81081,
82082, 83083, 84084, 85085, 86086, 87087, 88088.
Note that for symmetry reasons the code [9=0+] would also produce a maximum of 128 terms:
S’(5) = 10192, 10293, 10394, 10495, 10596, 10697,
10798, 11911, 12912, 13913, 14914, 15915, 16916, 17917, 18918, 19191, 20193,
20294, 20395, 20496, 20597, 20698, 21921, 22922, 23923, 24924, 25925, 26926,
27927, 28928, 29101, 29292, 30194, 30295, 30396, 30497, 30598, 31931, 32932,
33933, 34934, 35935, 36936, 37937, 38938, 39102, 39201, 39393, 40195, 40296,
40397, 40498, 41941, 42942, 43943, 44944, 45945, 46946, 47947, 48948, 49103,
49202, 49301, 49494, 50196, 50297, 50398, 51951, 52952, 53953, 54954, 55955,
56956, 57957, 58958, 59104, 59203, 59302, 59401, 59595, 60197, 60298, 61961,
62962, 63963, 64964, 65965, 66966, 67967, 68968, 69105, 69204, 69303, 69402,
69501, 69696, 70198, 71971, 72972, 73973, 74974, 75975, 76976, 77977, 78978,
79106, 79205, 79304, 79403, 79502, 79601, 79797, 81981, 82982, 83983, 84984,
85985, 86986, 87987, 88988, 89107, 89206, 89305, 89404, 89503, 89602, 89701,
89898.
Number
of 6-digit solutions:
=\+ 0
1 2 3
4 5 6
7 8
1 0
2 54 0
3 52
0 48
4 50
0 46 44
5 48
0 46 44
42
6 48
0 42 42 44
44
7 46
0 42 44
40 42 40
8 44
0 44 42
40 40 36
36
9 42
0 42 40
38 38 36
34 30
Maximum
(54):
1 11=3+8
2 11=4+7
3 11=5+6
4 11=6+5
5 11=7+4
6 11=8+3
7 13=4+9
8 13=5+8
9 13=6+7
10
13=7+6
11
13=8+5
12 13=9+4
13
14=5+9
14
14=6+8
15
14=7+7
16
14=8+6
17
14=9+5
18
15=6+9
19
15=7+8
20
15=8+7
21
15=9+6
22
16=7+9
23
16=8+8
24
16=9+7
25
17=8+9
26
17=9+8
27
18=9+9
28
3+8=11
29
4+7=11
30
4+9=13
31
5+6=11
32
5+8=13
33
5+9=14
34
6+5=11
35
6+7=13
36
6+8=14
37
6+9=15
38
7+4=11
39
7+6=13
40
7+7=14
41
7+8=15
42
7+9=16
43
8+3=11
44
8+5=13
45
8+6=14
46
8+7=15
47
8+8=16
48
8+9=17
49
9+4=13
50
9+5=14
51
9+6=15
52
9+7=16
53
9+8=17
54
9+9=18
This
gives the longest finite sequence of 6-digit integers, the code [0=2+] producing
a maximum of 54 terms:
S(6) = 110328, 110427, 110526,
110625, 110724, 110823, 130429, 130528, 130627, 130726, 130825, 130924, 140529,
140628, 140727, 140826, 140925, 150629, 150728, 150827, 150926, 160729, 160828,
160927, 170829, 170928, 180929, 328011, 427011, 429013, 526011, 528013, 529014,
625011, 627013, 628014, 629015, 724011, 726013, 727014, 728015, 729016, 823011,
825013, 826014, 827015, 828016, 829017, 924013, 925014, 926015, 927016, 928017,
929018.
Note that for symmetry reasons the code [2=0+] would also produce a maximum of 54 terms:
S’(6) = 112308, 112407,
112506, 112605, 112704, 112803, 132409, 132508, 132607, 132706, 132805, 132904,
142509, 142608, 142707, 142806, 142905, 152609, 152708, 152807, 152906, 162709,
162808, 162907, 172809, 172908, 182909, 308211, 407211, 409213, 506211, 508213,
509214, 605211, 607213, 608214, 609215, 704211, 706213, 707214, 708215, 709216,
803211, 805213, 806214, 807215, 808216, 809217, 904213, 905214, 906215, 907216,
908217, 909218.
Number
of 7-digit solutions:
=\+ 0
1 2 3
4 5 6
7 8
1 2423
2 2328
2143
3 2345
2089 2108
4 2364
2104 2004 2156
5 2352
2112 2039 2070
2179
6 2397
2135 2058 2058 2084
2182
7 2418
2154 2095 2084
2099 2121 2232
8 2439
2179 2084 2111
2107 2152 2167
2282
9 2544 2260 2195
2220 2243 2255
2282 2309 2376
Maximum
(2544):
#1
1+1+1=3 #2 1+1+2=4 #3 1+1+3=5
#4 1+1+4=6 #5 1+1+5=7 #6 1+1+6=8
#7 1+11=12 #8 1+12=13 #9 1+13=14
#10 1+14=15 #11 1+15=16 #12 1+16=17
#13 1+17=18 #14 1+1=1+1 #15 1+1=2=2
#16 1+2+1=4 #17 1+2+2=5 #18 1+2+3=6
#19 1+2+4=7 #20 1+2+5=8 #21 1+21=22
#22 1+22=23 #23 1+23=24 #24 1+24=25
#25 1+25=26 #26 1+26=27 #27 1+27=28
#28 1+2=1+2 #29 1+2=2+1 #30 1+2=3=3
#31 1+3+1=5 #32 1+3+2=6 #33 1+3+3=7
#34 1+3+4=8 #35 1+31=32 #36 1+32=33
#37 1+33=34 #38 1+34=35 #39 1+35=36
#40 1+36=37 #41 1+37=38 #42 1+3=1+3
#43 1+3=2+2 #44 1+3=3+1 #45 1+3=4=4
#46 1+4+1=6 #47 1+4+2=7 #48 1+4+3=8
#49 1+41=42 #50 1+42=43 #51 1+43=44
#52 1+44=45 #53 1+45=46 #54 1+46=47
#55 1+47=48 #56 1+4=1+4 #57 1+4=2+3
#58 1+4=3+2 #59 1+4=4+1 #60 1+4=5=5
#61 1+5+1=7 #62 1+5+2=8 #63 1+51=52
#64 1+52=53 #65 1+53=54 #66 1+54=55
#67 1+55=56 #68 1+56=57 #69 1+57=58
#70 1+5=1+5 #71 1+5=2+4 #72 1+5=3+3
#73 1+5=4+2 #74 1+5=5+1 #75 1+5=6=6
#76 1+6+1=8 #77 1+61=62 #78 1+62=63
#79 1+63=64 #80 1+64=65 #81 1+65=66
#82 1+66=67 #83 1+67=68 #84 1+6=1+6
#85 1+6=2+5 #86 1+6=3+4 #87 1+6=4+3
#88 1+6=5+2 #89 1+6=6+1 #90 1+6=7=7
#91 1+71=72 #92 1+72=73 #93 1+73=74
#94 1+74=75 #95 1+75=76 #96 1+76=77
#97 1+77=78 #98 1+7=1+7 #99 1+7=2+6
#100 1+7=3+5 #101 1+7=4+4 #102 1+7=5+3
#103 1+7=6+2 #104 1+7=7+1 #105 1+7=8=8
#106 1+81=82 #107 1+82=83 #108 1+83=84
#109 1+84=85 #110 1+85=86 #111 1+86=87
#112 1+87=88 #113 1+8=1+8 #114 1+8=2+7
#115 1+8=3+6 #116 1+8=4+5 #117 1+8=5+4
#118 1+8=6+3 #119 1+8=7+2 #120 1+8=8+1
#121 11+1=12 #122 11+2=13 #123 11+3=14
#124 11+4=15 #125 11+5=16 #126 11+6=17
#127 11+7=18 #128 111=111 #129 112=112
#130 113=113 #131 114=114 #132 115=115
#133 116=116 #134 117=117 #135 118=118
#136 12+1=13 #137 12+2=14 #138 12+3=15
#139 12+4=16 #140 12+5=17 #141 12+6=18
#142 121=121 #143 122=122 #144 123=123
#145 124=124 #146 125=125 #147 126=126
#148 127=127 #149 128=128 #150 12=1+11
#151 12=11+1 #152 13+1=14 #153 13+2=15
#154 13+3=16 #155 13+4=17 #156 13+5=18
#157 13+8=21 #158 131=131 #159 132=132
#160 133=133 #161 134=134 #162 135=135
#163 136=136 #164 137=137 #165 138=138
#166 13=1+12 #167 13=11+2 #168 13=12+1
#169 13=2+11 #170 14+1=15 #171 14+2=16
#172 14+3=17 #173 14+4=18 #174 14+7=21
#175 14+8=22 #176 141=141 #177 142=142
#178 143=143 #179 144=144 #180 145=145
#181 146=146 #182 147=147 #183 148=148
#184 14=1+13 #185 14=11+3 #186 14=12+2
#187 14=13+1 #188 14=2+12 #189 14=3+11
#190 15+1=16 #191 15+2=17 #192 15+3=18
#193 15+6=21 #194 15+7=22 #195 15+8=23
#196 151=151 #197 152=152 #198 153=153
#199 154=154 #200 155=155 #201 156=156
#202 157=157 #203 158=158 #204 15=1+14
#205 15=11+4 #206 15=12+3 #207 15=13+2
#208 15=14+1 #209 15=2+13 #210 15=3+12
#211 15=4+11 #212 16+1=17 #213 16+2=18
#214 16+5=21 #215 16+6=22 #216 16+7=23
#217 16+8=24 #218 161=161 #219 162=162
#220 163=163 #221 164=164 #222 165=165
#223 166=166 #224 167=167 #225 168=168
#226 16=1+15 #227 16=11+5 #228 16=12+4
#229 16=13+3 #230 16=14+2 #231 16=15+1
#232 16=2+14 #233 16=3+13 #234 16=4+12
#235 16=5+11 #236 17+1=18 #237 17+4=21
#238 17+5=22 #239 17+6=23 #240 17+7=24
#241 17+8=25 #242 171=171 #243 172=172
#244 173=173 #245 174=174 #246 175=175
#247 176=176 #248 177=177 #249 178=178
#250 17=1+16 #251 17=11+6 #252 17=12+5
#253 17=13+4 #254 17=14+3 #255 17=15+2
#256 17=16+1 #257 17=2+15 #258 17=3+14
#259 17=4+13 #260 17=5+12 #261 17=6+11
#262 18+3=21 #263 18+4=22 #264 18+5=23
#265 18+6=24 #266 18+7=25 #267 18+8=26
#268 181=181 #269 182=182 #270 183=183
#271 184=184 #272 185=185 #273 186=186
#274 187=187 #275 188=188 #276 18=1+17
#277 18=11+7 #278 18=12+6 #279 18=13+5
#280 18=14+4 #281 18=15+3 #282 18=16+2
#283 18=17+1 #284 18=2+16 #285 18=3+15
#286 18=4+14 #287 18=5+13 #288 18=6+12
#289 18=7+11 #290 1=1=1=1 #291 2+1+1=4
#292 2+1+2=5 #293 2+1+3=6 #294 2+1+4=7
#295 2+1+5=8 #296 2+11=13 #297 2+12=14
#298 2+13=15 #299 2+14=16 #300 2+15=17
#301 2+16=18 #302 2+1=1+2 #303 2+1=2+1
#304 2+1=3=3 #305 2+2+1=5 #306 2+2+2=6
#307 2+2+3=7 #308 2+2+4=8 #309 2+21=23
#310 2+22=24 #311 2+23=25 #312 2+24=26
#313 2+25=27 #314 2+26=28 #315 2+2=1+3
#316 2+2=2+2 #317 2+2=3+1 #318 2+2=4=4
#319 2+3+1=6 #320 2+3+2=7 #321 2+3+3=8
#322 2+31=33 #323 2+32=34 #324 2+33=35
#325 2+34=36 #326 2+35=37 #327 2+36=38
#328 2+3=1+4 #329 2+3=2+3 #330 2+3=3+2
#331 2+3=4+1 #332 2+3=5=5 #333 2+4+1=7
#334 2+4+2=8 #335 2+41=43 #336 2+42=44
#337 2+43=45 #338 2+44=46 #339 2+45=47
#340 2+46=48 #341 2+4=1+5 #342 2+4=2+4
#343 2+4=3+3 #344 2+4=4+2 #345 2+4=5+1
#346 2+4=6=6 #347 2+5+1=8 #348 2+51=53
#349 2+52=54 #350 2+53=55 #351 2+54=56
#352 2+55=57 #353 2+56=58 #354 2+5=1+6
#355 2+5=2+5 #356 2+5=3+4 #357 2+5=4+3
#358 2+5=5+2 #359 2+5=6+1 #360 2+5=7=7
#361 2+61=63 #362 2+62=64 #363 2+63=65
#364 2+64=66 #365 2+65=67 #366 2+66=68
#367 2+6=1+7 #368 2+6=2+6 #369 2+6=3+5
#370 2+6=4+4 #371 2+6=5+3 #372 2+6=6+2
#373 2+6=7+1 #374 2+6=8=8 #375 2+71=73
#376 2+72=74 #377 2+73=75 #378 2+74=76
#379 2+75=77 #380 2+76=78 #381 2+7=1+8
#382 2+7=2+7 #383 2+7=3+6 #384 2+7=4+5
#385 2+7=5+4 #386 2+7=6+3 #387 2+7=7+2
#388 2+7=8+1 #389 2+81=83 #390 2+82=84
#391 2+83=85 #392 2+84=86 #393 2+85=87
#394 2+86=88 #395 2+8=2+8 #396 2+8=3+7
#397 2+8=4+6 #398 2+8=5+5 #399 2+8=6+4
#400 2+8=7+3 #401 2+8=8+2 #402 21+1=22
#403 21+2=23 #404 21+3=24 #405 21+4=25
#406 21+5=26 #407 21+6=27 #408 21+7=28
#409 211=211 #410 212=212 #411 213=213
#412 214=214 #413 215=215 #414 216=216
#415 217=217 #416 218=218 #417 21=13+8
#418 21=14+7 #419 21=15+6 #420 21=16+5
#421 21=17+4 #422 21=18+3 #423 21=3+18
#424 21=4+17 #425 21=5+16 #426 21=6+15
#427 21=7+14 #428 21=8+13 #429 22+1=23
#430 22+2=24 #431 22+3=25 #432 22+4=26
#433 22+5=27 #434 22+6=28 #435 221=221
#436 222=222 #437 223=223 #438 224=224
#439 225=225 #440 226=226 #441 227=227
#442 228=228 #443 22=1+21 #444 22=14+8
#445 22=15+7 #446 22=16+6 #447 22=17+5
#448 22=18+4 #449 22=21+1 #450 22=4+18
#451 22=5+17 #452 22=6+16 #453 22=7+15
#454 22=8+14 #455 23+1=24 #456 23+2=25
#457 23+3=26 #458 23+4=27 #459 23+5=28
#460 23+8=31 #461 231=231 #462 232=232
#463 233=233 #464 234=234 #465 235=235
#466 236=236 #467 237=237 #468 238=238
#469 23=1+22 #470 23=15+8 #471 23=16+7
#472 23=17+6 #473 23=18+5 #474 23=2+21
#475 23=21+2 #476 23=22+1 #477 23=5+18
#478 23=6+17 #479 23=7+16 #480 23=8+15
#481 24+1=25 #482 24+2=26 #483 24+3=27
#484 24+4=28 #485 24+7=31 #486 24+8=32
#487 241=241 #488 242=242 #489 243=243
#490 244=244 #491 245=245 #492 246=246
#493 247=247 #494 248=248 #495 24=1+23
#496 24=16+8 #497 24=17+7 #498 24=18+6
#499 24=2+22 #500 24=21+3 #501 24=22+2
#502 24=23+1 #503 24=3+21 #504 24=6+18
#505 24=7+17 #506 24=8+16 #507 25+1=26
#508 25+2=27 #509 25+3=28 #510 25+6=31
#511 25+7=32 #512 25+8=33 #513 251=251
#514 252=252 #515 253=253 #516 254=254
#517 255=255 #518 256=256 #519 257=257
#520 258=258 #521 25=1+24 #522 25=17+8
#523 25=18+7 #524 25=2+23 #525 25=21+4
#526 25=22+3 #527 25=23+2 #528 25=24+1
#529 25=3+22 #530 25=4+21 #531 25=7+18
#532 25=8+17 #533 26+1=27 #534 26+2=28
#535 26+5=31 #536 26+6=32 #537 26+7=33
#538 26+8=34 #539 261=261 #540 262=262
#541 263=263 #542 264=264 #543 265=265
#544 266=266 #545 267=267 #546 268=268
#547 26=1+25 #548 26=18+8 #549 26=2+24
#550 26=21+5 #551 26=22+4 #552 26=23+3
#553 26=24+2 #554 26=25+1 #555 26=3+23
#556 26=4+22 #557 26=5+21 #558 26=8+18
#559 27+1=28 #560 27+4=31 #561 27+5=32
#562 27+6=33 #563 27+7=34 #564 27+8=35
#565 271=271 #566 272=272 #567 273=273
#568 274=274 #569 275=275 #570 276=276
#571 277=277 #572 278=278 #573 27=1+26
#574 27=2+25 #575 27=21+6 #576 27=22+5
#577 27=23+4 #578 27=24+3 #579 27=25+2
#580 27=26+1 #581 27=3+24 #582 27=4+23
#583 27=5+22 #584 27=6+21 #585 28+3=31
#586 28+4=32 #587 28+5=33 #588 28+6=34
#589 28+7=35 #590 28+8=36 #591 281=281
#592 282=282 #593 283=283 #594 284=284
#595 285=285 #596 286=286 #597 287=287
#598 288=288 #599 28=1+27 #600 28=2+26
#601 28=21+7 #602 28=22+6 #603 28=23+5
#604 28=24+4 #605 28=25+3 #606 28=26+2
#607 28=27+1 #608 28=3+25 #609 28=4+24
#610 28=5+23 #611 28=6+22 #612 28=7+21
#613 2=1+1=2 #614 2=2=1+1 #615 2=2=2=2
#616 3+1+1=5 #617 3+1+2=6 #618 3+1+3=7
#619 3+1+4=8 #620 3+11=14 #621 3+12=15
#622 3+13=16 #623 3+14=17 #624 3+15=18
#625 3+18=21 #626 3+1=1+3 #627 3+1=2+2
#628 3+1=3+1 #629 3+1=4=4 #630 3+2+1=6
#631 3+2+2=7 #632 3+2+3=8 #633 3+21=24
#634 3+22=25 #635 3+23=26 #636 3+24=27
#637 3+25=28 #638 3+28=31 #639 3+2=1+4
#640 3+2=2+3 #641 3+2=3+2 #642 3+2=4+1
#643 3+2=5=5 #644 3+3+1=7 #645 3+3+2=8
#646 3+31=34 #647 3+32=35 #648 3+33=36
#649 3+34=37 #650 3+35=38 #651 3+38=41
#652 3+3=1+5 #653 3+3=2+4 #654 3+3=3+3
#655 3+3=4+2 #656 3+3=5+1 #657 3+3=6=6
#658 3+4+1=8 #659 3+41=44 #660 3+42=45
#661 3+43=46 #662 3+44=47 #663 3+45=48
#664 3+48=51 #665 3+4=1+6 #666 3+4=2+5
#667 3+4=3+4 #668 3+4=4+3 #669 3+4=5+2
#670 3+4=6+1 #671 3+4=7=7 #672 3+51=54
#673 3+52=55 #674 3+53=56 #675 3+54=57
#676 3+55=58 #677 3+58=61 #678 3+5=1+7
#679 3+5=2+6 #680 3+5=3+5 #681 3+5=4+4
#682 3+5=5+3 #683 3+5=6+2 #684 3+5=7+1
#685 3+5=8=8 #686 3+61=64 #687 3+62=65
#688 3+63=66 #689 3+64=67 #690 3+65=68
#691 3+68=71 #692 3+6=1+8 #693 3+6=2+7
#694 3+6=3+6 #695 3+6=4+5 #696 3+6=5+4
#697 3+6=6+3 #698 3+6=7+2 #699 3+6=8+1
#700 3+71=74 #701 3+72=75 #702 3+73=76
#703 3+74=77 #704 3+75=78 #705 3+78=81
#706 3+7=2+8 #707 3+7=3+7 #708 3+7=4+6
#709 3+7=5+5 #710 3+7=6+4 #711 3+7=7+3
#712 3+7=8+2 #713 3+81=84 #714 3+82=85
#715 3+83=86 #716 3+84=87 #717 3+85=88
#718 3+8=3+8 #719 3+8=4+7 #720 3+8=5+6
#721 3+8=6+5 #722 3+8=7+4 #723 3+8=8+3
#724 31+1=32 #725 31+2=33 #726 31+3=34
#727 31+4=35 #728 31+5=36 #729 31+6=37
#730 31+7=38 #731 311=311 #732 312=312
#733 313=313 #734 314=314 #735 315=315
#736 316=316 #737 317=317 #738 318=318
#739 31=23+8 #740 31=24+7 #741 31=25+6
#742 31=26+5 #743 31=27+4 #744 31=28+3
#745 31=3+28 #746 31=4+27 #747 31=5+26
#748 31=6+25 #749 31=7+24 #750 31=8+23
#751 32+1=33 #752 32+2=34 #753 32+3=35
#754 32+4=36 #755 32+5=37 #756 32+6=38
#757 321=321 #758 322=322 #759 323=323
#760 324=324 #761 325=325 #762 326=326
#763 327=327 #764 328=328 #765 32=1+31
#766 32=24+8 #767 32=25+7 #768 32=26+6
#769 32=27+5 #770 32=28+4 #771 32=31+1
#772 32=4+28 #773 32=5+27 #774 32=6+26
#775 32=7+25 #776 32=8+24 #777 33+1=34
#778 33+2=35 #779 33+3=36 #780 33+4=37
#781 33+5=38 #782 33+8=41 #783 331=331
#784 332=332 #785 333=333 #786 334=334
#787 335=335 #788 336=336 #789 337=337
#790 338=338 #791 33=1+32 #792 33=2+31
#793 33=25+8 #794 33=26+7 #795 33=27+6
#796 33=28+5 #797 33=31+2 #798 33=32+1
#799 33=5+28 #800 33=6+27 #801 33=7+26
#802 33=8+25 #803 34+1=35 #804 34+2=36
#805 34+3=37 #806 34+4=38 #807 34+7=41
#808 34+8=42 #809 341=341 #810 342=342
#811 343=343 #812 344=344 #813 345=345
#814 346=346 #815 347=347 #816 348=348
#817 34=1+33 #818 34=2+32 #819 34=26+8
#820 34=27+7 #821 34=28+6 #822 34=3+31
#823 34=31+3 #824 34=32+2 #825 34=33+1
#826 34=6+28 #827 34=7+27 #828 34=8+26
#829 35+1=36 #830 35+2=37 #831 35+3=38
#832 35+6=41 #833 35+7=42 #834 35+8=43
#835 351=351 #836 352=352 #837 353=353
#838 354=354 #839 355=355 #840 356=356
#841 357=357 #842 358=358 #843 35=1+34
#844 35=2+33 #845 35=27+8 #846 35=28+7
#847 35=3+32 #848 35=31+4 #849 35=32+3
#850 35=33+2 #851 35=34+1 #852 35=4+31
#853 35=7+28 #854 35=8+27 #855 36+1=37
#856 36+2=38 #857 36+5=41 #858 36+6=42
#859 36+7=43 #860 36+8=44 #861 361=361
#862 362=362 #863 363=363 #864 364=364
#865 365=365 #866 366=366 #867 367=367
#868 368=368 #869 36=1+35 #870 36=2+34
#871 36=28+8 #872 36=3+33 #873 36=31+5
#874 36=32+4 #875 36=33+3 #876 36=34+2
#877 36=35+1 #878 36=4+32 #879 36=5+31
#880 36=8+28 #881 37+1=38 #882 37+4=41
#883 37+5=42 #884 37+6=43 #885 37+7=44
#886 37+8=45 #887 371=371 #888 372=372
#889 373=373 #890 374=374 #891 375=375
#892 376=376 #893 377=377 #894 378=378
#895 37=1+36 #896 37=2+35 #897 37=3+34
#898 37=31+6 #899 37=32+5 #900 37=33+4
#901 37=34+3 #902 37=35+2 #903 37=36+1
#904 37=4+33 #905 37=5+32 #906 37=6+31
#907 38+3=41 #908 38+4=42 #909 38+5=43
#910 38+6=44 #911 38+7=45 #912 38+8=46
#913 381=381 #914 382=382 #915 383=383
#916 384=384 #917 385=385 #918 386=386
#919 387=387 #920 388=388 #921 38=1+37
#922 38=2+36 #923 38=3+35 #924 38=31+7
#925 38=32+6 #926 38=33+5 #927 38=34+4
#928 38=35+3 #929 38=36+2 #930 38=37+1
#931 38=4+34 #932 38=5+33 #933 38=6+32
#934 38=7+31 #935 3=1+1+1 #936 3=1+2=3
#937 3=2+1=3 #938 3=3=1+2 #939 3=3=2+1
#940 3=3=3=3 #941 4+1+1=6 #942 4+1+2=7
#943 4+1+3=8 #944 4+11=15 #945 4+12=16
#946 4+13=17 #947 4+14=18 #948 4+17=21
#949 4+18=22 #950 4+1=1+4 #951 4+1=2+3
#952 4+1=3+2 #953 4+1=4+1 #954 4+1=5=5
#955 4+2+1=7 #956 4+2+2=8 #957 4+21=25
#958 4+22=26 #959 4+23=27 #960 4+24=28
#961 4+27=31 #962 4+28=32 #963 4+2=1+5
#964 4+2=2+4 #965 4+2=3+3 #966 4+2=4+2
#967 4+2=5+1 #968 4+2=6=6 #969 4+3+1=8
#970 4+31=35 #971 4+32=36 #972 4+33=37
#973 4+34=38 #974 4+37=41 #975 4+38=42
#976 4+3=1+6 #977 4+3=2+5 #978 4+3=3+4
#979 4+3=4+3 #980 4+3=5+2 #981 4+3=6+1
#982 4+3=7=7 #983 4+41=45 #984 4+42=46
#985 4+43=47 #986 4+44=48 #987 4+47=51
#988 4+48=52 #989 4+4=1+7 #990 4+4=2+6
#991 4+4=3+5 #992 4+4=4+4 #993 4+4=5+3
#994 4+4=6+2 #995 4+4=7+1 #996 4+4=8=8
#997 4+51=55 #998 4+52=56 #999 4+53=57
#1000 4+54=58 #1001 4+57=61 #1002 4+58=62
#1003 4+5=1+8 #1004 4+5=2+7 #1005 4+5=3+6
#1006 4+5=4+5 #1007 4+5=5+4 #1008 4+5=6+3
#1009 4+5=7+2 #1010 4+5=8+1 #1011 4+61=65
#1012 4+62=66 #1013 4+63=67 #1014 4+64=68
#1015 4+67=71 #1016 4+68=72 #1017 4+6=2+8
#1018 4+6=3+7 #1019 4+6=4+6 #1020 4+6=5+5
#1021 4+6=6+4 #1022 4+6=7+3 #1023 4+6=8+2
#1024 4+71=75 #1025 4+72=76 #1026 4+73=77
#1027 4+74=78 #1028 4+77=81 #1029 4+78=82
#1030 4+7=3+8 #1031 4+7=4+7 #1032 4+7=5+6
#1033 4+7=6+5 #1034 4+7=7+4 #1035 4+7=8+3
#1036 4+81=85 #1037 4+82=86 #1038 4+83=87
#1039 4+84=88 #1040 4+8=4+8 #1041 4+8=5+7
#1042 4+8=6+6 #1043 4+8=7+5 #1044 4+8=8+4
#1045 41+1=42 #1046 41+2=43 #1047 41+3=44
#1048 41+4=45 #1049 41+5=46 #1050 41+6=47
#1051 41+7=48 #1052 411=411 #1053 412=412
#1054 413=413 #1055 414=414 #1056 415=415
#1057 416=416 #1058 417=417 #1059 418=418
#1060 41=3+38 #1061 41=33+8 #1062 41=34+7
#1063 41=35+6 #1064 41=36+5 #1065 41=37+4
#1066 41=38+3 #1067 41=4+37 #1068 41=5+36
#1069 41=6+35 #1070 41=7+34 #1071 41=8+33
#1072 42+1=43 #1073 42+2=44 #1074 42+3=45
#1075 42+4=46 #1076 42+5=47 #1077 42+6=48
#1078 421=421 #1079 422=422 #1080 423=423
#1081 424=424 #1082 425=425 #1083 426=426
#1084 427=427 #1085 428=428 #1086 42=1+41
#1087 42=34+8 #1088 42=35+7 #1089 42=36+6
#1090 42=37+5 #1091 42=38+4 #1092 42=4+38
#1093 42=41+1 #1094 42=5+37 #1095 42=6+36
#1096 42=7+35 #1097 42=8+34 #1098 43+1=44
#1099 43+2=45 #1100 43+3=46 #1101 43+4=47
#1102 43+5=48 #1103 43+8=51 #1104 431=431
#1105 432=432 #1106 433=433 #1107 434=434
#1108 435=435 #1109 436=436 #1110 437=437
#1111 438=438 #1112 43=1+42 #1113 43=2+41
#1114 43=35+8 #1115 43=36+7 #1116 43=37+6
#1117 43=38+5 #1118 43=41+2 #1119 43=42+1
#1120 43=5+38 #1121 43=6+37 #1122 43=7+36
#1123 43=8+35 #1124 44+1=45 #1125 44+2=46
#1126 44+3=47 #1127 44+4=48 #1128 44+7=51
#1129 44+8=52 #1130 441=441 #1131 442=442
#1132 443=443 #1133 444=444 #1134 445=445
#1135 446=446 #1136 447=447 #1137 448=448
#1138 44=1+43 #1139 44=2+42 #1140 44=3+41
#1141 44=36+8 #1142 44=37+7 #1143 44=38+6
#1144 44=41+3 #1145 44=42+2 #1146 44=43+1
#1147 44=6+38 #1148 44=7+37 #1149 44=8+36
#1150 45+1=46 #1151 45+2=47 #1152 45+3=48
#1153 45+6=51 #1154 45+7=52 #1155 45+8=53
#1156 451=451 #1157 452=452 #1158 453=453
#1159 454=454 #1160 455=455 #1161 456=456
#1162 457=457 #1163 458=458 #1164 45=1+44
#1165 45=2+43 #1166 45=3+42 #1167 45=37+8
#1168 45=38+7 #1169 45=4+41 #1170 45=41+4
#1171 45=42+3 #1172 45=43+2 #1173 45=44+1
#1174 45=7+38 #1175 45=8+37 #1176 46+1=47
#1177 46+2=48 #1178 46+5=51 #1179 46+6=52
#1180 46+7=53 #1181 46+8=54 #1182 461=461
#1183 462=462 #1184 463=463 #1185 464=464
#1186 465=465 #1187 466=466 #1188 467=467
#1189 468=468 #1190 46=1+45 #1191 46=2+44
#1192 46=3+43 #1193 46=38+8 #1194 46=4+42
#1195 46=41+5 #1196 46=42+4 #1197 46=43+3
#1198 46=44+2 #1199 46=45+1 #1200 46=5+41
#1201 46=8+38 #1202 47+1=48 #1203 47+4=51
#1204 47+5=52 #1205 47+6=53 #1206 47+7=54
#1207 47+8=55 #1208 471=471 #1209 472=472
#1210 473=473 #1211 474=474 #1212 475=475
#1213 476=476 #1214 477=477 #1215 478=478
#1216 47=1+46 #1217 47=2+45 #1218 47=3+44
#1219 47=4+43 #1220 47=41+6 #1221 47=42+5
#1222 47=43+4 #1223 47=44+3 #1224 47=45+2
#1225 47=46+1 #1226 47=5+42 #1227 47=6+41
#1228 48+3=51 #1229 48+4=52 #1230 48+5=53
#1231 48+6=54 #1232 48+7=55 #1233 48+8=56
#1234 481=481 #1235 482=482 #1236 483=483
#1237 484=484 #1238 485=485 #1239 486=486
#1240 487=487 #1241 488=488 #1242 48=1+47
#1243 48=2+46 #1244 48=3+45 #1245 48=4+44
#1246 48=41+7 #1247 48=42+6 #1248 48=43+5
#1249 48=44+4 #1250 48=45+3 #1251 48=46+2
#1252 48=47+1 #1253 48=5+43 #1254 48=6+42
#1255 48=7+41 #1256 4=1+1+2 #1257 4=1+2+1
#1258 4=1+3=4 #1259 4=2+1+1 #1260 4=2+2=4
#1261 4=3+1=4 #1262 4=4=1+3 #1263 4=4=2+2
#1264 4=4=3+1 #1265 4=4=4=4 #1266 5+1+1=7
#1267 5+1+2=8 #1268 5+11=16 #1269 5+12=17
#1270 5+13=18 #1271 5+16=21 #1272 5+17=22
#1273 5+18=23 #1274 5+1=1+5 #1275 5+1=2+4
#1276 5+1=3+3 #1277 5+1=4+2 #1278 5+1=5+1
#1279 5+1=6=6 #1280 5+2+1=8 #1281 5+21=26
#1282 5+22=27 #1283 5+23=28 #1284 5+26=31
#1285 5+27=32 #1286 5+28=33 #1287 5+2=1+6
#1288 5+2=2+5 #1289 5+2=3+4 #1290 5+2=4+3
#1291 5+2=5+2 #1292 5+2=6+1 #1293 5+2=7=7
#1294 5+31=36 #1295 5+32=37 #1296 5+33=38
#1297 5+36=41 #1298 5+37=42 #1299 5+38=43
#1300 5+3=1+7 #1301 5+3=2+6 #1302 5+3=3+5
#1303 5+3=4+4 #1304 5+3=5+3 #1305 5+3=6+2
#1306 5+3=7+1 #1307 5+3=8=8 #1308 5+41=46
#1309 5+42=47 #1310 5+43=48 #1311 5+46=51
#1312 5+47=52 #1313 5+48=53 #1314 5+4=1+8
#1315 5+4=2+7 #1316 5+4=3+6 #1317 5+4=4+5
#1318 5+4=5+4 #1319 5+4=6+3 #1320 5+4=7+2
#1321 5+4=8+1 #1322 5+51=56 #1323 5+52=57
#1324 5+53=58 #1325 5+56=61 #1326 5+57=62
#1327 5+58=63 #1328 5+5=2+8 #1329 5+5=3+7
#1330 5+5=4+6 #1331 5+5=5+5 #1332 5+5=6+4
#1333 5+5=7+3 #1334 5+5=8+2 #1335 5+61=66
#1336 5+62=67 #1337 5+63=68 #1338 5+66=71
#1339 5+67=72 #1340 5+68=73 #1341 5+6=3+8
#1342 5+6=4+7 #1343 5+6=5+6 #1344 5+6=6+5
#1345 5+6=7+4 #1346 5+6=8+3 #1347 5+71=76
#1348 5+72=77 #1349 5+73=78 #1350 5+76=81
#1351 5+77=82 #1352 5+78=83 #1353 5+7=4+8
#1354 5+7=5+7 #1355 5+7=6+6 #1356 5+7=7+5
#1357 5+7=8+4 #1358 5+81=86 #1359 5+82=87
#1360 5+83=88 #1361 5+8=5+8 #1362 5+8=6+7
#1363 5+8=7+6 #1364 5+8=8+5 #1365 51+1=52
#1366 51+2=53 #1367 51+3=54 #1368 51+4=55
#1369 51+5=56 #1370 51+6=57 #1371 51+7=58
#1372 511=511 #1373 512=512 #1374 513=513
#1375 514=514 #1376 515=515 #1377 516=516
#1378 517=517 #1379 518=518 #1380 51=3+48
#1381 51=4+47 #1382 51=43+8 #1383 51=44+7
#1384 51=45+6 #1385 51=46+5 #1386 51=47+4
#1387 51=48+3 #1388 51=5+46 #1389 51=6+45
#1390 51=7+44 #1391 51=8+43 #1392 52+1=53
#1393 52+2=54 #1394 52+3=55 #1395 52+4=56
#1396 52+5=57 #1397 52+6=58 #1398 521=521
#1399 522=522 #1400 523=523 #1401 524=524
#1402 525=525 #1403 526=526 #1404 527=527
#1405 528=528 #1406 52=1+51 #1407 52=4+48
#1408 52=44+8 #1409 52=45+7 #1410 52=46+6
#1411 52=47+5 #1412 52=48+4 #1413 52=5+47
#1414 52=51+1 #1415 52=6+46 #1416 52=7+45
#1417 52=8+44 #1418 53+1=54 #1419 53+2=55
#1420 53+3=56 #1421 53+4=57 #1422 53+5=58
#1423 53+8=61 #1424 531=531 #1425 532=532
#1426 533=533 #1427 534=534 #1428 535=535
#1429 536=536 #1430 537=537 #1431 538=538
#1432 53=1+52 #1433 53=2+51 #1434 53=45+8
#1435 53=46+7 #1436 53=47+6 #1437 53=48+5
#1438 53=5+48 #1439 53=51+2 #1440 53=52+1 #1441 53=6+47
#1442 53=7+46 #1443 53=8+45 #1444 54+1=55
#1445 54+2=56 #1446 54+3=57 #1447 54+4=58
#1448 54+7=61 #1449 54+8=62 #1450 541=541
#1451 542=542 #1452 543=543 #1453 544=544
#1454 545=545 #1455 546=546 #1456 547=547
#1457 548=548 #1458 54=1+53 #1459 54=2+52
#1460 54=3+51 #1461 54=46+8 #1462 54=47+7
#1463 54=48+6 #1464 54=51+3 #1465 54=52+2
#1466 54=53+1 #1467 54=6+48 #1468 54=7+47
#1469 54=8+46 #1470 55+1=56 #1471 55+2=57
#1472 55+3=58 #1473 55+6=61 #1474 55+7=62
#1475 55+8=63 #1476 551=551 #1477 552=552
#1478 553=553 #1479 554=554 #1480 555=555
#1481 556=556 #1482 557=557 #1483 558=558
#1484 55=1+54 #1485 55=2+53 #1486 55=3+52
#1487 55=4+51 #1488 55=47+8 #1489 55=48+7
#1490 55=51+4 #1491 55=52+3 #1492 55=53+2
#1493 55=54+1 #1494 55=7+48 #1495 55=8+47
#1496 56+1=57 #1497 56+2=58 #1498 56+5=61
#1499 56+6=62 #1500 56+7=63 #1501 56+8=64
#1502 561=561 #1503 562=562 #1504 563=563
#1505 564=564 #1506 565=565 #1507 566=566
#1508 567=567 #1509 568=568 #1510 56=1+55
#1511 56=2+54 #1512 56=3+53 #1513 56=4+52
#1514 56=48+8 #1515 56=5+51 #1516 56=51+5
#1517 56=52+4 #1518 56=53+3 #1519 56=54+2
#1520 56=55+1 #1521 56=8+48 #1522 57+1=58
#1523 57+4=61 #1524 57+5=62 #1525 57+6=63
#1526 57+7=64 #1527 57+8=65 #1528 571=571
#1529 572=572 #1530 573=573 #1531 574=574
#1532 575=575 #1533 576=576 #1534 577=577
#1535 578=578 #1536 57=1+56 #1537 57=2+55
#1538 57=3+54 #1539 57=4+53 #1540 57=5+52
#1541 57=51+6 #1542 57=52+5 #1543 57=53+4
#1544 57=54+3 #1545 57=55+2 #1546 57=56+1
#1547 57=6+51 #1548 58+3=61 #1549 58+4=62
#1550 58+5=63 #1551 58+6=64 #1552 58+7=65
#1553 58+8=66 #1554 581=581 #1555 582=582
#1556 583=583 #1557 584=584 #1558 585=585
#1559 586=586 #1560 587=587 #1561 588=588
#1562 58=1+57 #1563 58=2+56 #1564 58=3+55
#1565 58=4+54 #1566 58=5+53 #1567 58=51+7
#1568 58=52+6 #1569 58=53+5 #1570 58=54+4
#1571 58=55+3 #1572 58=56+2 #1573 58=57+1
#1574 58=6+52 #1575 58=7+51 #1576 5=1+1+3
#1577 5=1+2+2 #1578 5=1+3+1 #1579 5=1+4=5
#1580 5=2+1+2 #1581 5=2+2+1 #1582 5=2+3=5
#1583 5=3+1+1 #1584 5=3+2=5 #1585 5=4+1=5
#1586 5=5=1+4 #1587 5=5=2+3 #1588 5=5=3+2
#1589 5=5=4+1 #1590 5=5=5=5 #1591 6+1+1=8
#1592 6+11=17 #1593 6+12=18 #1594 6+15=21
#1595 6+16=22 #1596 6+17=23 #1597 6+18=24
#1598 6+1=1+6 #1599 6+1=2+5 #1600 6+1=3+4
#1601 6+1=4+3 #1602 6+1=5+2 #1603 6+1=6+1
#1604 6+1=7=7 #1605 6+21=27 #1606 6+22=28
#1607 6+25=31 #1608 6+26=32 #1609 6+27=33
#1610 6+28=34 #1611 6+2=1+7 #1612 6+2=2+6
#1613 6+2=3+5 #1614 6+2=4+4 #1615 6+2=5+3
#1616 6+2=6+2 #1617 6+2=7+1 #1618 6+2=8=8
#1619 6+31=37 #1620 6+32=38 #1621 6+35=41
#1622 6+36=42 #1623 6+37=43 #1624 6+38=44
#1625 6+3=1+8 #1626 6+3=2+7 #1627 6+3=3+6
#1628 6+3=4+5 #1629 6+3=5+4 #1630 6+3=6+3
#1631 6+3=7+2 #1632 6+3=8+1 #1633 6+41=47
#1634 6+42=48 #1635 6+45=51 #1636 6+46=52
#1637 6+47=53 #1638 6+48=54 #1639 6+4=2+8
#1640 6+4=3+7 #1641 6+4=4+6 #1642 6+4=5+5
#1643 6+4=6+4 #1644 6+4=7+3 #1645 6+4=8+2
#1646 6+51=57 #1647 6+52=58 #1648 6+55=61
#1649 6+56=62 #1650 6+57=63 #1651 6+58=64
#1652 6+5=3+8 #1653 6+5=4+7 #1654 6+5=5+6
#1655 6+5=6+5 #1656 6+5=7+4 #1657 6+5=8+3
#1658 6+61=67 #1659 6+62=68 #1660 6+65=71
#1661 6+66=72 #1662 6+67=73 #1663 6+68=74
#1664 6+6=4+8 #1665 6+6=5+7 #1666 6+6=6+6
#1667 6+6=7+5 #1668 6+6=8+4 #1669 6+71=77
#1670 6+72=78 #1671 6+75=81 #1672 6+76=82
#1673 6+77=83 #1674 6+78=84 #1675 6+7=5+8
#1676 6+7=6+7 #1677 6+7=7+6 #1678 6+7=8+5
#1679 6+81=87 #1680 6+82=88 #1681 6+8=6+8
#1682 6+8=7+7 #1683 6+8=8+6 #1684 61+1=62
#1685 61+2=63 #1686 61+3=64 #1687 61+4=65
#1688 61+5=66 #1689 61+6=67 #1690 61+7=68
#1691 611=611 #1692 612=612 #1693 613=613
#1694 614=614 #1695 615=615 #1696 616=616 #1697 617=617
#1698 618=618 #1699 61=3+58 #1700 61=4+57
#1701 61=5+56 #1702 61=53+8 #1703 61=54+7
#1704 61=55+6 #1705 61=56+5 #1706 61=57+4
#1707 61=58+3 #1708 61=6+55 #1709 61=7+54
#1710 61=8+53 #1711 62+1=63 #1712 62+2=64
#1713 62+3=65 #1714 62+4=66 #1715 62+5=67
#1716 62+6=68 #1717 621=621 #1718 622=622
#1719 623=623 #1720 624=624 #1721 625=625
#1722 626=626 #1723 627=627 #1724 628=628
#1725 62=1+61 #1726 62=4+58 #1727 62=5+57
#1728 62=54+8 #1729 62=55+7 #1730 62=56+6
#1731 62=57+5 #1732 62=58+4 #1733 62=6+56
#1734 62=61+1 #1735 62=7+55 #1736 62=8+54
#1737 63+1=64 #1738 63+2=65 #1739 63+3=66
#1740 63+4=67 #1741 63+5=68 #1742 63+8=71
#1743 631=631 #1744 632=632 #1745 633=633
#1746 634=634 #1747 635=635 #1748 636=636
#1749 637=637 #1750 638=638 #1751 63=1+62
#1752 63=2+61 #1753 63=5+58 #1754 63=55+8
#1755 63=56+7 #1756 63=57+6 #1757 63=58+5
#1758 63=6+57 #1759 63=61+2 #1760 63=62+1
#1761 63=7+56 #1762 63=8+55 #1763 64+1=65
#1764 64+2=66 #1765 64+3=67 #1766 64+4=68
#1767 64+7=71 #1768 64+8=72 #1769 641=641
#1770 642=642 #1771 643=643 #1772 644=644
#1773 645=645 #1774 646=646 #1775 647=647
#1776 648=648 #1777 64=1+63 #1778 64=2+62
#1779 64=3+61 #1780 64=56+8 #1781 64=57+7
#1782 64=58+6 #1783 64=6+58 #1784 64=61+3
#1785 64=62+2 #1786 64=63+1 #1787 64=7+57
#1788 64=8+56 #1789 65+1=66 #1790 65+2=67
#1791 65+3=68 #1792 65+6=71 #1793 65+7=72
#1794 65+8=73 #1795 651=651 #1796 652=652
#1797 653=653 #1798 654=654 #1799 655=655
#1800 656=656 #1801 657=657 #1802 658=658
#1803 65=1+64 #1804 65=2+63 #1805 65=3+62
#1806 65=4+61 #1807 65=57+8 #1808 65=58+7
#1809 65=61+4 #1810 65=62+3 #1811 65=63+2
#1812 65=64+1 #1813 65=7+58 #1814 65=8+57
#1815 66+1=67 #1816 66+2=68 #1817 66+5=71
#1818 66+6=72 #1819 66+7=73 #1820 66+8=74
#1821 661=661 #1822 662=662 #1823 663=663
#1824 664=664 #1825 665=665 #1826 666=666
#1827 667=667 #1828 668=668 #1829 66=1+65
#1830 66=2+64 #1831 66=3+63 #1832 66=4+62
#1833 66=5+61 #1834 66=58+8 #1835 66=61+5
#1836 66=62+4 #1837 66=63+3 #1838 66=64+2
#1839 66=65+1 #1840 66=8+58 #1841 67+1=68
#1842 67+4=71 #1843 67+5=72 #1844 67+6=73
#1845 67+7=74 #1846 67+8=75 #1847 671=671
#1848 672=672 #1849 673=673 #1850 674=674
#1851 675=675 #1852 676=676 #1853 677=677
#1854 678=678 #1855 67=1+66 #1856 67=2+65
#1857 67=3+64 #1858 67=4+63 #1859 67=5+62
#1860 67=6+61 #1861 67=61+6 #1862 67=62+5
#1863 67=63+4 #1864 67=64+3 #1865 67=65+2
#1866 67=66+1 #1867 68+3=71 #1868 68+4=72
#1869 68+5=73 #1870 68+6=74 #1871 68+7=75
#1872 68+8=76 #1873 681=681 #1874 682=682
#1875 683=683 #1876 684=684 #1877 685=685
#1878 686=686 #1879 687=687 #1880 688=688
#1881 68=1+67 #1882 68=2+66 #1883 68=3+65
#1884 68=4+64 #1885 68=5+63 #1886 68=6+62
#1887 68=61+7 #1888 68=62+6 #1889 68=63+5
#1890 68=64+4 #1891 68=65+3 #1892 68=66+2
#1893 68=67+1 #1894 68=7+61 #1895 6=1+1+4
#1896 6=1+2+3 #1897 6=1+3+2 #1898 6=1+4+1
#1899 6=1+5=6 #1900 6=2+1+3 #1901 6=2+2+2
#1902 6=2+3+1 #1903 6=2+4=6 #1904 6=3+1+2
#1905 6=3+2+1 #1906 6=3+3=6 #1907 6=4+1+1
#1908 6=4+2=6 #1909 6=5+1=6 #1910 6=6=1+5
#1911 6=6=2+4 #1912 6=6=3+3 #1913 6=6=4+2
#1914 6=6=5+1 #1915 6=6=6=6 #1916 7+11=18
#1917 7+14=21 #1918 7+15=22 #1919 7+16=23
#1920 7+17=24 #1921 7+18=25 #1922 7+1=1+7
#1923 7+1=2+6 #1924 7+1=3+5 #1925 7+1=4+4
#1926 7+1=5+3 #1927 7+1=6+2 #1928 7+1=7+1
#1929 7+1=8=8 #1930 7+21=28 #1931 7+24=31
#1932 7+25=32 #1933 7+26=33 #1934 7+27=34
#1935 7+28=35 #1936 7+2=1+8 #1937 7+2=2+7
#1938 7+2=3+6 #1939 7+2=4+5 #1940 7+2=5+4
#1941 7+2=6+3 #1942 7+2=7+2 #1943 7+2=8+1
#1944 7+31=38 #1945 7+34=41 #1946 7+35=42
#1947 7+36=43 #1948 7+37=44 #1949 7+38=45
#1950 7+3=2+8 #1951 7+3=3+7 #1952 7+3=4+6 #1953 7+3=5+5
#1954 7+3=6+4 #1955 7+3=7+3 #1956 7+3=8+2
#1957 7+41=48 #1958 7+44=51 #1959 7+45=52
#1960 7+46=53 #1961 7+47=54 #1962 7+48=55
#1963 7+4=3+8 #1964 7+4=4+7 #1965 7+4=5+6
#1966 7+4=6+5 #1967 7+4=7+4 #1968 7+4=8+3
#1969 7+51=58 #1970 7+54=61 #1971 7+55=62
#1972 7+56=63 #1973 7+57=64 #1974 7+58=65
#1975 7+5=4+8 #1976 7+5=5+7 #1977 7+5=6+6
#1978 7+5=7+5 #1979 7+5=8+4 #1980 7+61=68
#1981 7+64=71 #1982 7+65=72 #1983 7+66=73
#1984 7+67=74 #1985 7+68=75 #1986 7+6=5+8
#1987 7+6=6+7 #1988 7+6=7+6 #1989 7+6=8+5
#1990 7+71=78 #1991 7+74=81 #1992 7+75=82
#1993 7+76=83 #1994 7+77=84 #1995 7+78=85
#1996 7+7=6+8 #1997 7+7=7+7 #1998 7+7=8+6
#1999 7+81=88 #2000 7+8=7+8 #2001 7+8=8+7
#2002 71+1=72 #2003 71+2=73 #2004 71+3=74
#2005 71+4=75 #2006 71+5=76 #2007 71+6=77
#2008 71+7=78 #2009 711=711 #2010 712=712
#2011 713=713 #2012 714=714 #2013 715=715
#2014 716=716 #2015 717=717 #2016 718=718
#2017 71=3+68 #2018 71=4+67 #2019 71=5+66
#2020 71=6+65 #2021 71=63+8 #2022 71=64+7
#2023 71=65+6 #2024 71=66+5 #2025 71=67+4
#2026 71=68+3 #2027 71=7+64 #2028 71=8+63
#2029 72+1=73 #2030 72+2=74 #2031 72+3=75
#2032 72+4=76 #2033 72+5=77 #2034 72+6=78
#2035 721=721 #2036 722=722 #2037 723=723
#2038 724=724 #2039 725=725 #2040 726=726
#2041 727=727 #2042 728=728 #2043 72=1+71
#2044 72=4+68 #2045 72=5+67 #2046 72=6+66
#2047 72=64+8 #2048 72=65+7 #2049 72=66+6
#2050 72=67+5 #2051 72=68+4 #2052 72=7+65
#2053 72=71+1 #2054 72=8+64 #2055 73+1=74
#2056 73+2=75 #2057 73+3=76 #2058 73+4=77
#2059 73+5=78 #2060 73+8=81 #2061 731=731
#2062 732=732 #2063 733=733 #2064 734=734
#2065 735=735 #2066 736=736 #2067 737=737
#2068 738=738 #2069 73=1+72 #2070 73=2+71
#2071 73=5+68 #2072 73=6+67 #2073 73=65+8
#2074 73=66+7 #2075 73=67+6 #2076 73=68+5
#2077 73=7+66 #2078 73=71+2 #2079 73=72+1
#2080 73=8+65 #2081 74+1=75 #2082 74+2=76
#2083 74+3=77 #2084 74+4=78 #2085 74+7=81
#2086 74+8=82 #2087 741=741 #2088 742=742
#2089 743=743 #2090 744=744 #2091 745=745
#2092 746=746 #2093 747=747 #2094 748=748
#2095 74=1+73 #2096 74=2+72 #2097 74=3+71
#2098 74=6+68 #2099 74=66+8 #2100 74=67+7
#2101 74=68+6 #2102 74=7+67 #2103 74=71+3
#2104 74=72+2 #2105 74=73+1 #2106 74=8+66
#2107 75+1=76 #2108 75+2=77 #2109 75+3=78
#2110 75+6=81 #2111 75+7=82 #2112 75+8=83
#2113 751=751 #2114 752=752 #2115 753=753
#2116 754=754 #2117 755=755 #2118 756=756
#2119 757=757 #2120 758=758 #2121 75=1+74
#2122 75=2+73 #2123 75=3+72 #2124 75=4+71
#2125 75=67+8 #2126 75=68+7 #2127 75=7+68
#2128 75=71+4 #2129 75=72+3 #2130 75=73+2
#2131 75=74+1 #2132 75=8+67 #2133 76+1=77
#2134 76+2=78 #2135 76+5=81 #2136 76+6=82
#2137 76+7=83 #2138 76+8=84 #2139 761=761
#2140 762=762 #2141 763=763 #2142 764=764
#2143 765=765 #2144 766=766 #2145 767=767
#2146 768=768 #2147 76=1+75 #2148 76=2+74
#2149 76=3+73 #2150 76=4+72 #2151 76=5+71
#2152 76=68+8 #2153 76=71+5 #2154 76=72+4
#2155 76=73+3 #2156 76=74+2 #2157 76=75+1
#2158 76=8+68 #2159 77+1=78 #2160 77+4=81
#2161 77+5=82 #2162 77+6=83 #2163 77+7=84
#2164 77+8=85 #2165 771=771 #2166 772=772
#2167 773=773 #2168 774=774 #2169 775=775
#2170 776=776 #2171 777=777 #2172 778=778
#2173 77=1+76 #2174 77=2+75 #2175 77=3+74
#2176 77=4+73 #2177 77=5+72 #2178 77=6+71
#2179 77=71+6 #2180 77=72+5 #2181 77=73+4
#2182 77=74+3 #2183 77=75+2 #2184 77=76+1
#2185 78+3=81 #2186 78+4=82 #2187 78+5=83
#2188 78+6=84 #2189 78+7=85 #2190 78+8=86
#2191 781=781 #2192 782=782 #2193 783=783
#2194 784=784 #2195 785=785 #2196 786=786
#2197 787=787 #2198 788=788 #2199 78=1+77
#2200 78=2+76 #2201 78=3+75 #2202 78=4+74
#2203 78=5+73 #2204 78=6+72 #2205 78=7+71
#2206 78=71+7 #2207 78=72+6 #2208 78=73+5 #2209 78=74+4
#2210 78=75+3 #2211 78=76+2 #2212 78=77+1
#2213 7=1+1+5 #2214 7=1+2+4 #2215 7=1+3+3
#2216 7=1+4+2 #2217 7=1+5+1 #2218 7=1+6=7
#2219 7=2+1+4 #2220 7=2+2+3 #2221 7=2+3+2
#2222 7=2+4+1 #2223 7=2+5=7 #2224 7=3+1+3
#2225 7=3+2+2 #2226 7=3+3+1 #2227 7=3+4=7
#2228 7=4+1+2 #2229 7=4+2+1 #2230 7=4+3=7
#2231 7=5+1+1 #2232 7=5+2=7 #2233 7=6+1=7
#2234 7=7=1+6 #2235 7=7=2+5 #2236 7=7=3+4
#2237 7=7=4+3 #2238 7=7=5+2 #2239 7=7=6+1
#2240 7=7=7=7 #2241 8+13=21 #2242 8+14=22
#2243 8+15=23 #2244 8+16=24 #2245 8+17=25
#2246 8+18=26 #2247 8+1=1+8 #2248 8+1=2+7
#2249 8+1=3+6 #2250 8+1=4+5 #2251 8+1=5+4
#2252 8+1=6+3 #2253 8+1=7+2 #2254 8+1=8+1
#2255 8+23=31 #2256 8+24=32 #2257 8+25=33
#2258 8+26=34 #2259 8+27=35 #2260 8+28=36
#2261 8+2=2+8 #2262 8+2=3+7 #2263 8+2=4+6
#2264 8+2=5+5 #2265 8+2=6+4 #2266 8+2=7+3
#2267 8+2=8+2 #2268 8+33=41 #2269 8+34=42
#2270 8+35=43 #2271 8+36=44 #2272 8+37=45
#2273 8+38=46 #2274 8+3=3+8 #2275 8+3=4+7
#2276 8+3=5+6 #2277 8+3=6+5 #2278 8+3=7+4
#2279 8+3=8+3 #2280 8+43=51 #2281 8+44=52
#2282 8+45=53 #2283 8+46=54 #2284 8+47=55
#2285 8+48=56 #2286 8+4=4+8 #2287 8+4=5+7
#2288 8+4=6+6 #2289 8+4=7+5 #2290 8+4=8+4
#2291 8+53=61 #2292 8+54=62 #2293 8+55=63
#2294 8+56=64 #2295 8+57=65 #2296 8+58=66
#2297 8+5=5+8 #2298 8+5=6+7 #2299 8+5=7+6
#2300 8+5=8+5 #2301 8+63=71 #2302 8+64=72
#2303 8+65=73 #2304 8+66=74 #2305 8+67=75
#2306 8+68=76 #2307 8+6=6+8 #2308 8+6=7+7
#2309 8+6=8+6 #2310 8+73=81 #2311 8+74=82
#2312 8+75=83 #2313 8+76=84 #2314 8+77=85
#2315 8+78=86 #2316 8+7=7+8 #2317 8+7=8+7
#2318 8+8=8+8 #2319 81+1=82 #2320 81+2=83
#2321 81+3=84 #2322 81+4=85 #2323 81+5=86
#2324 81+6=87 #2325 81+7=88 #2326 811=811
#2327 812=812 #2328 813=813 #2329 814=814
#2330 815=815 #2331 816=816 #2332 817=817
#2333 818=818 #2334 81=3+78 #2335 81=4+77
#2336 81=5+76 #2337 81=6+75 #2338 81=7+74
#2339 81=73+8 #2340 81=74+7 #2341 81=75+6
#2342 81=76+5 #2343 81=77+4 #2344 81=78+3
#2345 81=8+73 #2346 82+1=83 #2347 82+2=84
#2348 82+3=85 #2349 82+4=86 #2350 82+5=87
#2351 82+6=88 #2352 821=821 #2353 822=822
#2354 823=823 #2355 824=824 #2356 825=825
#2357 826=826 #2358 827=827 #2359 828=828
#2360 82=1+81 #2361 82=4+78 #2362 82=5+77
#2363 82=6+76 #2364 82=7+75 #2365 82=74+8
#2366 82=75+7 #2367 82=76+6 #2368 82=77+5
#2369 82=78+4 #2370 82=8+74 #2371 82=81+1
#2372 83+1=84 #2373 83+2=85 #2374 83+3=86
#2375 83+4=87 #2376 83+5=88 #2377 831=831
#2378 832=832 #2379 833=833 #2380 834=834
#2381 835=835 #2382 836=836 #2383 837=837
#2384 838=838 #2385 83=1+82 #2386 83=2+81
#2387 83=5+78 #2388 83=6+77 #2389 83=7+76
#2390 83=75+8 #2391 83=76+7 #2392 83=77+6
#2393 83=78+5 #2394 83=8+75 #2395 83=81+2
#2396 83=82+1 #2397 84+1=85 #2398 84+2=86
#2399 84+3=87 #2400 84+4=88 #2401 841=841
#2402 842=842 #2403 843=843 #2404 844=844
#2405 845=845 #2406 846=846 #2407 847=847
#2408 848=848 #2409 84=1+83 #2410 84=2+82
#2411 84=3+81 #2412 84=6+78 #2413 84=7+77
#2414 84=76+8 #2415 84=77+7 #2416 84=78+6
#2417 84=8+76 #2418 84=81+3 #2419 84=82+2
#2420 84=83+1 #2421 85+1=86 #2422 85+2=87
#2423 85+3=88 #2424 851=851 #2425 852=852
#2426 853=853 #2427 854=854 #2428 855=855
#2429 856=856 #2430 857=857 #2431 858=858
#2432 85=1+84 #2433 85=2+83 #2434 85=3+82
#2435 85=4+81 #2436 85=7+78 #2437 85=77+8
#2438 85=78+7 #2439 85=8+77 #2440 85=81+4
#2441 85=82+3 #2442 85=83+2 #2443 85=84+1
#2444 86+1=87 #2445 86+2=88 #2446 861=861
#2447 862=862 #2448 863=863 #2449 864=864
#2450 865=865 #2451 866=866 #2452 867=867
#2453 868=868 #2454 86=1+85 #2455 86=2+84
#2456 86=3+83 #2457 86=4+82 #2458 86=5+81
#2459 86=78+8 #2460 86=8+78 #2461 86=81+5
#2462 86=82+4 #2463 86=83+3 #2464 86=84+2 #2465 86=85+1
#2466 87+1=88 #2467 871=871 #2468 872=872
#2469 873=873 #2470 874=874 #2471 875=875
#2472 876=876 #2473 877=877 #2474 878=878
#2475 87=1+86 #2476 87=2+85 #2477 87=3+84
#2478 87=4+83 #2479 87=5+82 #2480 87=6+81
#2481 87=81+6 #2482 87=82+5 #2483 87=83+4
#2484 87=84+3 #2485 87=85+2 #2486 87=86+1
#2487 881=881 #2488 882=882 #2489 883=883
#2490 884=884 #2491 885=885 #2492 886=886
#2493 887=887 #2494 888=888 #2495 88=1+87
#2496 88=2+86 #2497 88=3+85 #2498 88=4+84
#2499 88=5+83 #2500 88=6+82 #2501 88=7+81
#2502 88=81+7 #2503 88=82+6 #2504 88=83+5
#2505 88=84+4 #2506 88=85+3 #2507 88=86+2
#2508 88=87+1 #2509 8=1+1+6 #2510 8=1+2+5
#2511 8=1+3+4 #2512 8=1+4+3 #2513 8=1+5+2
#2514 8=1+6+1 #2515 8=1+7=8 #2516 8=2+1+5
#2517 8=2+2+4 #2518 8=2+3+3 #2519 8=2+4+2
#2520 8=2+5+1 #2521 8=2+6=8 #2522 8=3+1+4
#2523 8=3+2+3 #2524 8=3+3+2 #2525 8=3+4+1
#2526 8=3+5=8 #2527 8=4+1+3 #2528 8=4+2+2
#2529 8=4+3+1 #2530 8=4+4=8 #2531 8=5+1+2
#2532 8=5+2+1 #2533 8=5+3=8 #2534 8=6+1+1
#2535 8=6+2=8 #2536 8=7+1=8 #2537 8=8=1+7
#2538 8=8=2+6 #2539 8=8=3+5 #2540 8=8=4+4
#2541 8=8=5+3 #2542 8=8=6+2 #2543 8=8=7+1
#2544 8=8=8=8
This
gives the longest finite sequence of 7-digit integers, the code [0=9+] producing
a maximum of 2544 terms:
S(7) =.1010101, 1110111,
1120112, 1130113, 1140114, 1150115, 1160116, 1170117, 1180118, 1191012,
1192013, 1193014, 1194015, 1195016, 1196017, 1197018, 1201191, 1201911,
1210121, 1220122, 1230123, 1240124, 1250125, 1260126, 1270127, 1280128,
1291013, 1292014, 1293015, 1294016, 1295017, 1296018, 1301192, 1301291,
1301912, 1302911, 1310131, 1320132, 1330133, 1340134, 1350135, 1360136,
1370137, 1380138, 1391014, 1392015, 1393016, 1394017, 1395018, 1398021,
1401193, 1401292, 1401391, 1401913, 1402912, 1403911, 1410141, 1420142,
1430143, 1440144, 1450145, 1460146, 1470147, 1480148, 1491015, 1492016,
1493017, 1494018, 1497021, 1498022, 1501194, 1501293, 1501392, 1501491,
1501914, 1502913, 1503912, 1504911, 1510151, 1520152, 1530153, 1540154,
1550155, 1560156, 1570157, 1580158, 1591016, 1592017, 1593018, 1596021,
1597022, 1598023, 1601195, 1601294, 1601393, 1601492, 1601591, 1601915,
1602914, 1603913, 1604912, 1605911, 1610161, 1620162, 1630163, 1640164,
1650165, 1660166, 1670167, 1680168, 1691017, 1692018, 1695021, 1696022,
1697023, 1698024, 1701196, 1701295, 1701394, 1701493, 1701592, 1701691,
1701916, 1702915, 1703914, 1704913, 1705912, 1706911, 1710171, 1720172,
1730173, 1740174, 1750175, 1760176, 1770177, 1780178, 1791018, 1794021,
1795022, 1796023, 1797024, 1798025, 1801197, 1801296, 1801395, 1801494,
1801593, 1801692, 1801791, 1801917, 1802916, 1803915, 1804914, 1805913,
1806912, 1807911, 1810181, 1820182, 1830183, 1840184, 1850185, 1860186,
1870187, 1880188, 1893021, 1894022, 1895023, 1896024, 1897025, 1898026,
1910191, 1910202, 1911012, 1912013, 1913014, 1914015, 1915016, 1916017,
1917018, 1919103, 1919204, 1919305, 1919406, 1919507, 1919608, 1920192,
1920291, 1920303, 1921022, 1922023, 1923024, 1924025, 1925026, 1926027, 1927028,
1929104, 1929205, 1929306, 1929407, 1929508, 1930193, 1930292, 1930391,
1930404, 1931032, 1932033, 1933034, 1934035, 1935036, 1936037, 1937038,
1939105, 1939206, 1939307, 1939408, 1940194, 1940293, 1940392, 1940491,
1940505, 1941042, 1942043, 1943044, 1944045, 1945046, 1946047, 1947048,
1949106, 1949207, 1949308, 1950195, 1950294, 1950393, 1950492, 1950591,
1950606, 1951052, 1952053, 1953054, 1954055, 1955056, 1956057, 1957058,
1959107, 1959208, 1960196, 1960295, 1960394, 1960493, 1960592, 1960691, 1960707,
1961062, 1962063, 1963064, 1964065, 1965066, 1966067, 1967068, 1969108,
1970197, 1970296, 1970395, 1970494, 1970593, 1970692, 1970791, 1970808,
1971072, 1972073, 1973074, 1974075, 1975076, 1976077, 1977078, 1980198,
1980297, 1980396, 1980495, 1980594, 1980693, 1980792, 1980891, 1981082,
1982083, 1983084, 1984085, 1985086, 1986087, 1987088, 2019102, 2020191,
2020202, 2101398, 2101497, 2101596, 2101695, 2101794, 2101893, 2103918,
2104917, 2105916, 2106915, 2107914, 2108913, 2110211, 2120212, 2130213, 2140214,
2150215, 2160216, 2170217, 2180218, 2191022, 2192023, 2193024, 2194025,
2195026, 2196027, 2197028, 2201498, 2201597, 2201696, 2201795, 2201894,
2201921, 2202191, 2204918, 2205917, 2206916, 2207915, 2208914, 2210221,
2220222, 2230223, 2240224, 2250225, 2260226, 2270227, 2280228, 2291023,
2292024, 2293025, 2294026, 2295027, 2296028, 2301598, 2301697, 2301796,
2301895, 2301922, 2302192, 2302291, 2302921, 2305918, 2306917, 2307916,
2308915, 2310231, 2320232, 2330233, 2340234, 2350235, 2360236, 2370237, 2380238,
2391024, 2392025, 2393026, 2394027, 2395028, 2398031, 2401698, 2401797,
2401896, 2401923, 2402193, 2402292, 2402391, 2402922, 2403921, 2406918,
2407917, 2408916, 2410241, 2420242, 2430243, 2440244, 2450245, 2460246,
2470247, 2480248, 2491025, 2492026, 2493027, 2494028, 2497031, 2498032,
2501798, 2501897, 2501924, 2502194, 2502293, 2502392, 2502491, 2502923,
2503922, 2504921, 2507918, 2508917, 2510251, 2520252, 2530253, 2540254,
2550255, 2560256, 2570257, 2580258, 2591026, 2592027, 2593028, 2596031, 2597032,
2598033, 2601898, 2601925, 2602195, 2602294, 2602393, 2602492, 2602591,
2602924, 2603923, 2604922, 2605921, 2608918, 2610261, 2620262, 2630263,
2640264, 2650265, 2660266, 2670267, 2680268, 2691027, 2692028, 2695031,
2696032, 2697033, 2698034, 2701926, 2702196, 2702295, 2702394, 2702493,
2702592, 2702691, 2702925, 2703924, 2704923, 2705922, 2706921, 2710271,
2720272, 2730273, 2740274, 2750275, 2760276, 2770277, 2780278, 2791028,
2794031, 2795032, 2796033, 2797034, 2798035, 2801927, 2802197, 2802296, 2802395,
2802494, 2802593, 2802692, 2802791, 2802926, 2803925, 2804924, 2805923,
2806922, 2807921, 2810281, 2820282, 2830283, 2840284, 2850285, 2860286,
2870287, 2880288, 2893031, 2894032, 2895033, 2896034, 2897035, 2898036,
2910192, 2910291, 2910303, 2911013, 2912014, 2913015, 2914016, 2915017,
2916018, 2919104, 2919205, 2919306, 2919407, 2919508, 2920193, 2920292,
2920391, 2920404, 2921023, 2922024, 2923025, 2924026, 2925027, 2926028,
2929105, 2929206, 2929307, 2929408, 2930194, 2930293, 2930392, 2930491, 2930505,
2931033, 2932034, 2933035, 2934036, 2935037, 2936038, 2939106, 2939207,
2939308, 2940195, 2940294, 2940393, 2940492, 2940591, 2940606, 2941043,
2942044, 2943045, 2944046, 2945047, 2946048, 2949107, 2949208, 2950196,
2950295, 2950394, 2950493, 2950592, 2950691, 2950707, 2951053, 2952054,
2953055, 2954056, 2955057, 2956058, 2959108, 2960197, 2960296, 2960395,
2960494, 2960593, 2960692, 2960791, 2960808, 2961063, 2962064, 2963065,
2964066, 2965067, 2966068, 2970198, 2970297, 2970396, 2970495, 2970594,
2970693, 2970792, 2970891, 2971073, 2972074, 2973075, 2974076, 2975077,
2976078, 2980298, 2980397, 2980496, 2980595, 2980694, 2980793, 2980892,
2981083, 2982084, 2983085, 2984086, 2985087, 2986088, 3019191, 3019203,
3029103, 3030192, 3030291, 3030303, 3102398, 3102497, 3102596, 3102695,
3102794, 3102893, 3103928, 3104927, 3105926, 3106925, 3107924, 3108923,
3110311, 3120312, 3130313, 3140314, 3150315, 3160316, 3170317, 3180318,
3191032, 3192033, 3193034, 3194035, 3195036, 3196037, 3197038, 3201931, 3202498,
3202597, 3202696, 3202795, 3202894, 3203191, 3204928, 3205927, 3206926,
3207925, 3208924, 3210321, 3220322, 3230323, 3240324, 3250325, 3260326,
3270327, 3280328, 3291033, 3292034, 3293035, 3294036, 3295037, 3296038,
3301932, 3302598, 3302697, 3302796, 3302895, 3302931, 3303192, 3303291,
3305928, 3306927, 3307926, 3308925, 3310331, 3320332, 3330333, 3340334,
3350335, 3360336, 3370337, 3380338, 3391034, 3392035, 3393036, 3394037,
3395038, 3398041, 3401933, 3402698, 3402797, 3402896, 3402932, 3403193, 3403292,
3403391, 3403931, 3406928, 3407927, 3408926, 3410341, 3420342, 3430343,
3440344, 3450345, 3460346, 3470347, 3480348, 3491035, 3492036, 3493037,
3494038, 3497041, 3498042, 3501934, 3502798, 3502897, 3502933, 3503194,
3503293, 3503392, 3503491, 3503932, 3504931, 3507928, 3508927, 3510351,
3520352, 3530353, 3540354, 3550355, 3560356, 3570357, 3580358, 3591036,
3592037, 3593038, 3596041, 3597042, 3598043, 3601935, 3602898, 3602934,
3603195, 3603294, 3603393, 3603492, 3603591, 3603933, 3604932, 3605931, 3608928,
3610361, 3620362, 3630363, 3640364, 3650365, 3660366, 3670367, 3680368,
3691037, 3692038, 3695041, 3696042, 3697043, 3698044, 3701936, 3702935,
3703196, 3703295, 3703394, 3703493, 3703592, 3703691, 3703934, 3704933,
3705932, 3706931, 3710371, 3720372, 3730373, 3740374, 3750375, 3760376,
3770377, 3780378, 3791038, 3794041, 3795042, 3796043, 3797044, 3798045,
3801937, 3802936, 3803197, 3803296, 3803395, 3803494, 3803593, 3803692,
3803791, 3803935, 3804934, 3805933, 3806932, 3807931, 3810381, 3820382, 3830383,
3840384, 3850385, 3860386, 3870387, 3880388, 3893041, 3894042, 3895043,
3896044, 3897045, 3898046, 3910193, 3910292, 3910391, 3910404, 3911014,
3912015, 3913016, 3914017, 3915018, 3918021, 3919105, 3919206, 3919307,
3919408, 3920194, 3920293, 3920392, 3920491, 3920505, 3921024, 3922025,
3923026, 3924027, 3925028, 3928031, 3929106, 3929207, 3929308, 3930195,
3930294, 3930393, 3930492, 3930591, 3930606, 3931034, 3932035, 3933036,
3934037, 3935038, 3938041, 3939107, 3939208, 3940196, 3940295, 3940394, 3940493,
3940592, 3940691, 3940707, 3941044, 3942045, 3943046, 3944047, 3945048,
3948051, 3949108, 3950197, 3950296, 3950395, 3950494, 3950593, 3950692,
3950791, 3950808, 3951054, 3952055, 3953056, 3954057, 3955058, 3958061,
3960198, 3960297, 3960396, 3960495, 3960594, 3960693, 3960792, 3960891,
3961064, 3962065, 3963066, 3964067, 3965068, 3968071, 3970298, 3970397,
3970496, 3970595, 3970694, 3970793, 3970892, 3971074, 3972075, 3973076,
3974077, 3975078, 3978081, 3980398, 3980497, 3980596, 3980695, 3980794, 3980893,
3981084, 3982085, 3983086, 3984087, 3985088, 4019192, 4019291, 4019304,
4029191, 4029204, 4039104, 4040193, 4040292, 4040391, 4040404, 4103398,
4103497, 4103596, 4103695, 4103794, 4103893, 4103938, 4104937, 4105936,
4106935, 4107934, 4108933, 4110411, 4120412, 4130413, 4140414, 4150415,
4160416, 4170417, 4180418, 4191042, 4192043, 4193044, 4194045, 4195046,
4196047, 4197048, 4201941, 4203498, 4203597, 4203696, 4203795, 4203894,
4204191, 4204938, 4205937, 4206936, 4207935, 4208934, 4210421, 4220422, 4230423,
4240424, 4250425, 4260426, 4270427, 4280428, 4291043, 4292044, 4293045,
4294046, 4295047, 4296048, 4301942, 4302941, 4303598, 4303697, 4303796,
4303895, 4304192, 4304291, 4305938, 4306937, 4307936, 4308935, 4310431,
4320432, 4330433, 4340434, 4350435, 4360436, 4370437, 4380438, 4391044,
4392045, 4393046, 4394047, 4395048, 4398051, 4401943, 4402942, 4403698,
4403797, 4403896, 4403941, 4404193, 4404292, 4404391, 4406938, 4407937,
4408936, 4410441, 4420442, 4430443, 4440444, 4450445, 4460446, 4470447, 4480448,
4491045, 4492046, 4493047, 4494048, 4497051, 4498052, 4501944, 4502943,
4503798, 4503897, 4503942, 4504194, 4504293, 4504392, 4504491, 4504941,
4507938, 4508937, 4510451, 4520452, 4530453, 4540454, 4550455, 4560456,
4570457, 4580458, 4591046, 4592047, 4593048, 4596051, 4597052, 4598053,
4601945, 4602944, 4603898, 4603943, 4604195, 4604294, 4604393, 4604492,
4604591, 4604942, 4605941, 4608938, 4610461, 4620462, 4630463, 4640464,
4650465, 4660466, 4670467, 4680468, 4691047, 4692048, 4695051, 4696052,
4697053, 4698054, 4701946, 4702945, 4703944, 4704196, 4704295, 4704394,
4704493, 4704592, 4704691, 4704943, 4705942, 4706941, 4710471, 4720472,
4730473, 4740474, 4750475, 4760476, 4770477, 4780478, 4791048, 4794051,
4795052, 4796053, 4797054, 4798055, 4801947, 4802946, 4803945, 4804197,
4804296, 4804395, 4804494, 4804593, 4804692, 4804791, 4804944, 4805943,
4806942, 4807941, 4810481, 4820482, 4830483, 4840484, 4850485, 4860486,
4870487, 4880488, 4893051, 4894052, 4895053, 4896054, 4897055, 4898056, 4910194,
4910293, 4910392, 4910491, 4910505, 4911015, 4912016, 4913017, 4914018,
4917021, 4918022, 4919106, 4919207, 4919308, 4920195, 4920294, 4920393,
4920492, 4920591, 4920606, 4921025, 4922026, 4923027, 4924028, 4927031,
4928032, 4929107, 4929208, 4930196, 4930295, 4930394, 4930493, 4930592,
4930691, 4930707, 4931035, 4932036, 4933037, 4934038, 4937041, 4938042,
4939108, 4940197, 4940296, 4940395, 4940494, 4940593, 4940692, 4940791,
4940808, 4941045, 4942046, 4943047, 4944048, 4947051, 4948052, 4950198, 4950297,
4950396, 4950495, 4950594, 4950693, 4950792, 4950891, 4951055, 4952056,
4953057, 4954058, 4957061, 4958062, 4960298, 4960397, 4960496, 4960595,
4960694, 4960793, 4960892, 4961065, 4962066, 4963067, 4964068, 4967071,
4968072, 4970398, 4970497, 4970596, 4970695, 4970794, 4970893, 4971075,
4972076, 4973077, 4974078, 4977081, 4978082, 4980498, 4980597, 4980696,
4980795, 4980894, 4981085, 4982086, 4983087, 4984088, 5019193, 5019292,
5019391, 5019405, 5029192, 5029291, 5029305, 5039191, 5039205, 5049105, 5050194,
5050293, 5050392, 5050491, 5050505, 5103948, 5104398, 5104497, 5104596,
5104695, 5104794, 5104893, 5104947, 5105946, 5106945, 5107944, 5108943,
5110511, 5120512, 5130513, 5140514, 5150515, 5160516, 5170517, 5180518,
5191052, 5192053, 5193054, 5194055, 5195056, 5196057, 5197058, 5201951,
5204498, 5204597, 5204696, 5204795, 5204894, 5204948, 5205191, 5205947,
5206946, 5207945, 5208944, 5210521, 5220522, 5230523, 5240524, 5250525,
5260526, 5270527, 5280528, 5291053, 5292054, 5293055, 5294056, 5295057, 5296058,
5301952, 5302951, 5304598, 5304697, 5304796, 5304895, 5305192, 5305291,
5305948, 5306947, 5307946, 5308945, 5310531, 5320532, 5330533, 5340534,
5350535, 5360536, 5370537, 5380538, 5391054, 5392055, 5393056, 5394057,
5395058, 5398061, 5401953, 5402952, 5403951, 5404698, 5404797, 5404896,
5405193, 5405292, 5405391, 5406948, 5407947, 5408946, 5410541, 5420542,
5430543, 5440544, 5450545, 5460546, 5470547, 5480548, 5491055, 5492056,
5493057, 5494058, 5497061, 5498062, 5501954, 5502953, 5503952, 5504798, 5504897,
5504951, 5505194, 5505293, 5505392, 5505491, 5507948, 5508947, 5510551,
5520552, 5530553, 5540554, 5550555, 5560556, 5570557, 5580558, 5591056,
5592057, 5593058, 5596061, 5597062, 5598063, 5601955, 5602954, 5603953,
5604898, 5604952, 5605195, 5605294, 5605393, 5605492, 5605591, 5605951,
5608948, 5610561, 5620562, 5630563, 5640564, 5650565, 5660566, 5670567,
5680568, 5691057, 5692058, 5695061, 5696062, 5697063, 5698064, 5701956,
5702955, 5703954, 5704953, 5705196, 5705295, 5705394, 5705493, 5705592, 5705691,
5705952, 5706951, 5710571, 5720572, 5730573, 5740574, 5750575, 5760576,
5770577, 5780578, 5791058, 5794061, 5795062, 5796063, 5797064, 5798065,
5801957, 5802956, 5803955, 5804954, 5805197, 5805296, 5805395, 5805494,
5805593, 5805692, 5805791, 5805953, 5806952, 5807951, 5810581, 5820582,
5830583, 5840584, 5850585, 5860586, 5870587, 5880588, 5893061, 5894062,
5895063, 5896064, 5897065, 5898066, 5910195, 5910294, 5910393, 5910492,
5910591, 5910606, 5911016, 5912017, 5913018, 5916021, 5917022, 5918023, 5919107,
5919208, 5920196, 5920295, 5920394, 5920493, 5920592, 5920691, 5920707,
5921026, 5922027, 5923028, 5926031, 5927032, 5928033, 5929108, 5930197,
5930296, 5930395, 5930494, 5930593, 5930692, 5930791, 5930808, 5931036,
5932037, 5933038, 5936041, 5937042, 5938043, 5940198, 5940297, 5940396,
5940495, 5940594, 5940693, 5940792, 5940891, 5941046, 5942047, 5943048,
5946051, 5947052, 5948053, 5950298, 5950397, 5950496, 5950595, 5950694,
5950793, 5950892, 5951056, 5952057, 5953058, 5956061, 5957062, 5958063, 5960398,
5960497, 5960596, 5960695, 5960794, 5960893, 5961066, 5962067, 5963068,
5966071, 5967072, 5968073, 5970498, 5970597, 5970696, 5970795, 5970894,
5971076, 5972077, 5973078, 5976081, 5977082, 5978083, 5980598, 5980697,
5980796, 5980895, 5981086, 5982087, 5983088, 6019194, 6019293, 6019392,
6019491, 6019506, 6029193, 6029292, 6029391, 6029406, 6039192, 6039291,
6039306, 6049191, 6049206, 6059106, 6060195, 6060294, 6060393, 6060492,
6060591, 6060606, 6103958, 6104957, 6105398, 6105497, 6105596, 6105695,
6105794, 6105893, 6105956, 6106955, 6107954, 6108953, 6110611, 6120612,
6130613, 6140614, 6150615, 6160616, 6170617, 6180618, 6191062, 6192063,
6193064, 6194065, 6195066, 6196067, 6197068, 6201961, 6204958, 6205498,
6205597, 6205696, 6205795, 6205894, 6205957, 6206191, 6206956, 6207955,
6208954, 6210621, 6220622, 6230623, 6240624, 6250625, 6260626, 6270627,
6280628, 6291063, 6292064, 6293065, 6294066, 6295067, 6296068, 6301962,
6302961, 6305598, 6305697, 6305796, 6305895, 6305958, 6306192, 6306291, 6306957,
6307956, 6308955, 6310631, 6320632, 6330633, 6340634, 6350635, 6360636,
6370637, 6380638, 6391064, 6392065, 6393066, 6394067, 6395068, 6398071,
6401963, 6402962, 6403961, 6405698, 6405797, 6405896, 6406193, 6406292,
6406391, 6406958, 6407957, 6408956, 6410641, 6420642, 6430643, 6440644,
6450645, 6460646, 6470647, 6480648, 6491065, 6492066, 6493067, 6494068,
6497071, 6498072, 6501964, 6502963, 6503962, 6504961, 6505798, 6505897,
6506194, 6506293, 6506392, 6506491, 6507958, 6508957, 6510651, 6520652, 6530653,
6540654, 6550655, 6560656, 6570657, 6580658, 6591066, 6592067, 6593068,
6596071, 6597072, 6598073, 6601965, 6602964, 6603963, 6604962, 6605898,
6605961, 6606195, 6606294, 6606393, 6606492, 6606591, 6608958, 6610661,
6620662, 6630663, 6640664, 6650665, 6660666, 6670667, 6680668, 6691067,
6692068, 6695071, 6696072, 6697073, 6698074, 6701966, 6702965, 6703964,
6704963, 6705962, 6706196, 6706295, 6706394, 6706493, 6706592, 6706691,
6706961, 6710671, 6720672, 6730673, 6740674, 6750675, 6760676, 6770677, 6780678,
6791068, 6794071, 6795072, 6796073, 6797074, 6798075, 6801967, 6802966,
6803965, 6804964, 6805963, 6806197, 6806296, 6806395, 6806494, 6806593,
6806692, 6806791, 6806962, 6807961, 6810681, 6820682, 6830683, 6840684,
6850685, 6860686, 6870687, 6880688, 6893071, 6894072, 6895073, 6896074,
6897075, 6898076, 6910196, 6910295, 6910394, 6910493, 6910592, 6910691,
6910707, 6911017, 6912018, 6915021, 6916022, 6917023, 6918024, 6919108,
6920197, 6920296, 6920395, 6920494, 6920593, 6920692, 6920791, 6920808, 6921027,
6922028, 6925031, 6926032, 6927033, 6928034, 6930198, 6930297, 6930396,
6930495, 6930594, 6930693, 6930792, 6930891, 6931037, 6932038, 6935041,
6936042, 6937043, 6938044, 6940298, 6940397, 6940496, 6940595, 6940694,
6940793, 6940892, 6941047, 6942048, 6945051, 6946052, 6947053, 6948054,
6950398, 6950497, 6950596, 6950695, 6950794, 6950893, 6951057, 6952058,
6955061, 6956062, 6957063, 6958064, 6960498, 6960597, 6960696, 6960795,
6960894, 6961067, 6962068, 6965071, 6966072, 6967073, 6968074, 6970598, 6970697,
6970796, 6970895, 6971077, 6972078, 6975081, 6976082, 6977083, 6978084,
6980698, 6980797, 6980896, 6981087, 6982088, 7019195, 7019294, 7019393,
7019492, 7019591, 7019607, 7029194, 7029293, 7029392, 7029491, 7029507,
7039193, 7039292, 7039391, 7039407, 7049192, 7049291, 7049307, 7059191,
7059207, 7069107, 7070196, 7070295, 7070394, 7070493, 7070592, 7070691,
7070707, 7103968, 7104967, 7105966, 7106398, 7106497, 7106596, 7106695,
7106794, 7106893, 7106965, 7107964, 7108963, 7110711, 7120712, 7130713, 7140714,
7150715, 7160716, 7170717, 7180718, 7191072, 7192073, 7193074, 7194075,
7195076, 7196077, 7197078, 7201971, 7204968, 7205967, 7206498, 7206597,
7206696, 7206795, 7206894, 7206966, 7207191, 7207965, 7208964, 7210721,
7220722, 7230723, 7240724, 7250725, 7260726, 7270727, 7280728, 7291073,
7292074, 7293075, 7294076, 7295077, 7296078, 7301972, 7302971, 7305968,
7306598, 7306697, 7306796, 7306895, 7306967, 7307192, 7307291, 7307966,
7308965, 7310731, 7320732, 7330733, 7340734, 7350735, 7360736, 7370737, 7380738,
7391074, 7392075, 7393076, 7394077, 7395078, 7398081, 7401973, 7402972,
7403971, 7406698, 7406797, 7406896, 7406968, 7407193, 7407292, 7407391,
7407967, 7408966, 7410741, 7420742, 7430743, 7440744, 7450745, 7460746,
7470747, 7480748, 7491075, 7492076, 7493077, 7494078, 7497081, 7498082,
7501974, 7502973, 7503972, 7504971, 7506798, 7506897, 7507194, 7507293,
7507392, 7507491, 7507968, 7508967, 7510751, 7520752, 7530753, 7540754,
7550755, 7560756, 7570757, 7580758, 7591076, 7592077, 7593078, 7596081, 7597082,
7598083, 7601975, 7602974, 7603973, 7604972, 7605971, 7606898, 7607195,
7607294, 7607393, 7607492, 7607591, 7608968, 7610761, 7620762, 7630763,
7640764, 7650765, 7660766, 7670767, 7680768, 7691077, 7692078, 7695081,
7696082, 7697083, 7698084, 7701976, 7702975, 7703974, 7704973, 7705972,
7706971, 7707196, 7707295, 7707394, 7707493, 7707592, 7707691, 7710771,
7720772, 7730773, 7740774, 7750775, 7760776, 7770777, 7780778, 7791078,
7794081, 7795082, 7796083, 7797084, 7798085, 7801977, 7802976, 7803975,
7804974, 7805973, 7806972, 7807197, 7807296, 7807395, 7807494, 7807593,
7807692, 7807791, 7807971, 7810781, 7820782, 7830783, 7840784, 7850785,
7860786, 7870787, 7880788, 7893081, 7894082, 7895083, 7896084, 7897085,
7898086, 7910197, 7910296, 7910395, 7910494, 7910593, 7910692, 7910791,
7910808, 7911018, 7914021, 7915022, 7916023, 7917024, 7918025, 7920198,
7920297, 7920396, 7920495, 7920594, 7920693, 7920792, 7920891, 7921028,
7924031, 7925032, 7926033, 7927034, 7928035, 7930298, 7930397, 7930496, 7930595,
7930694, 7930793, 7930892, 7931038, 7934041, 7935042, 7936043, 7937044,
7938045, 7940398, 7940497, 7940596, 7940695, 7940794, 7940893, 7941048,
7944051, 7945052, 7946053, 7947054, 7948055, 7950498, 7950597, 7950696,
7950795, 7950894, 7951058, 7954061, 7955062, 7956063, 7957064, 7958065,
7960598, 7960697, 7960796, 7960895, 7961068, 7964071, 7965072, 7966073,
7967074, 7968075, 7970698, 7970797, 7970896, 7971078, 7974081, 7975082,
7976083, 7977084, 7978085, 7980798, 7980897, 7981088, 8019196, 8019295, 8019394,
8019493, 8019592, 8019691, 8019708, 8029195, 8029294, 8029393, 8029492,
8029591, 8029608, 8039194, 8039293, 8039392, 8039491, 8039508, 8049193,
8049292, 8049391, 8049408, 8059192, 8059291, 8059308, 8069191, 8069208,
8079108, 8080197, 8080296, 8080395, 8080494, 8080593, 8080692, 8080791,
8080808., 8103978, 8104977, 8105976, 8106975, 8107398, 8107497, 8107596, 8107695,
8107794, 8107893, 8107974, 8108973, 8110811, 8120812, 8130813, 8140814,
8150815, 8160816, 8170817, 8180818, 8191082, 8192083, 8193084, 8194085,
8195086, 8196087, 8197088, 8201981, 8204978, 8205977, 8206976, 8207498,
8207597, 8207696, 8207795, 8207894, 8207975, 8208191, 8208974, 8210821,
8220822, 8230823, 8240824, 8250825, 8260826, 8270827, 8280828, 8291083,
8292084, 8293085, 8294086, 8295087, 8296088, 8301982, 8302981, 8305978,
8306977, 8307598, 8307697, 8307796, 8307895, 8307976, 8308192, 8308291,
8308975, 8310831, 8320832, 8330833, 8340834, 8350835, 8360836, 8370837,
8380838, 8391084, 8392085, 8393086, 8394087, 8395088, 8401983, 8402982, 8403981,
8406978, 8407698, 8407797, 8407896, 8407977, 8408193, 8408292, 8408391,
8408976, 8410841, 8420842, 8430843, 8440844, 8450845, 8460846, 8470847,
8480848, 8491085, 8492086, 8493087, 8494088, 8501984, 8502983, 8503982,
8504981, 8507798, 8507897, 8507978, 8508194, 8508293, 8508392, 8508491,
8508977, 8510851, 8520852, 8530853, 8540854, 8550855, 8560856, 8570857,
8580858, 8591086, 8592087, 8593088, 8601985, 8602984, 8603983, 8604982,
8605981, 8607898, 8608195, 8608294, 8608393, 8608492, 8608591, 8608978, 8610861,
8620862, 8630863, 8640864, 8650865, 8660866, 8670867, 8680868, 8691087,
8692088, 8701986, 8702985, 8703984, 8704983, 8705982, 8706981, 8708196,
8708295, 8708394, 8708493, 8708592, 8708691, 8710871, 8720872, 8730873,
8740874, 8750875, 8760876, 8770877, 8780878, 8791088, 8801987, 8802986,
8803985, 8804984, 8805983, 8806982, 8807981, 8808197, 8808296, 8808395,
8808494, 8808593, 8808692, 8808791, 8810881, 8820882, 8830883, 8840884,
8850885, 8860886, 8870887, 8880888, 8910198, 8910297, 8910396, 8910495, 8910594,
8910693, 8910792, 8910891, 8913021, 8914022, 8915023, 8916024, 8917025,
8918026, 8920298, 8920397, 8920496, 8920595, 8920694, 8920793, 8920892,
8923031, 8924032, 8925033, 8926034, 8927035, 8928036, 8930398, 8930497,
8930596, 8930695, 8930794, 8930893, 8933041, 8934042, 8935043, 8936044,
8937045, 8938046, 8940498, 8940597, 8940696, 8940795, 8940894, 8943051,
8944052, 8945053, 8946054, 8947055, 8948056, 8950598, 8950697, 8950796,
8950895, 8953061, 8954062, 8955063, 8956064, 8957065, 8958066, 8960698, 8960797,
8960896, 8963071, 8964072, 8965073, 8966074, 8967075, 8968076, 8970798,
8970897, 8973081, 8974082, 8975083, 8976084, 8977085, 8978086, 8980898,
Note that for symmetry reasons the code [9=0+] would also produce a maximum of 2544 terms:
S’(7) = 1010193, 1010294,
1010395, 1010496, 1010597, 1010698, 1011912, 1012913, 1013914, 1014915,
1015916, 1016917, 1017918, 1019101, 1019292, 1020194, 1020295, 1020396,
1020497, 1020598, 1021922, 1022923, 1023924, 1024925, 1025926, 1026927,
1027928, 1029102, 1029201, 1029393, 1030195, 1030296, 1030397, 1030498,
1031932, 1032933, 1033934, 1034935, 1035936, 1036937, 1037938, 1039103,
1039202, 1039301, 1039494, 1040196, 1040297, 1040398, 1041942, 1042943,
1043944, 1044945, 1045946, 1046947, 1047948, 1049104, 1049203, 1049302,
1049401, 1049595, 1050197, 1050298, 1051952, 1052953, 1053954, 1054955,
1055956, 1056957, 1057958, 1059105, 1059204, 1059303, 1059402, 1059501,
1059696, 1060198, 1061962, 1062963, 1063964, 1064965, 1065966, 1066967,
1067968, 1069106, 1069205, 1069304, 1069403, 1069502, 1069601, 1069797,
1071972, 1072973, 1073974, 1074975, 1075976, 1076977, 1077978, 1079107,
1079206, 1079305, 1079404, 1079503, 1079602, 1079701, 1079898, 1081982,
1082983, 1083984, 1084985, 1085986, 1086987, 1087988, 1089108, 1089207,
1089306, 1089405, 1089504, 1089603, 1089702, 1089801, 1101912, 1102913,
1103914, 1104915, 1105916, 1106917, 1107918, 1119111, 1129112, 1139113,
1149114, 1159115, 1169116, 1179117, 1189118, 1201913, 1202914, 1203915,
1204916, 1205917, 1206918, 1219121, 1229122, 1239123, 1249124, 1259125,
1269126, 1279127, 1289128, 1291011, 1291101, 1301914, 1302915, 1303916,
1304917, 1305918, 1308921, 1319131, 1329132, 1339133, 1349134, 1359135,
1369136, 1379137, 1389138, 1391012, 1391102, 1391201, 1392011, 1401915, 1402916,
1403917, 1404918, 1407921, 1408922, 1419141, 1429142, 1439143, 1449144,
1459145, 1469146, 1479147, 1489148, 1491013, 1491103, 1491202, 1491301,
1492012, 1493011, 1501916, 1502917, 1503918, 1506921, 1507922, 1508923,
1519151, 1529152, 1539153, 1549154, 1559155, 1569156, 1579157, 1589158,
1591014, 1591104, 1591203, 1591302, 1591401, 1592013, 1593012, 1594011,
1601917, 1602918, 1605921, 1606922, 1607923, 1608924, 1619161, 1629162,
1639163, 1649164, 1659165, 1669166, 1679167, 1689168, 1691015, 1691105, 1691204,
1691303, 1691402, 1691501, 1692014, 1693013, 1694012, 1695011, 1701918,
1704921, 1705922, 1706923, 1707924, 1708925, 1719171, 1729172, 1739173,
1749174, 1759175, 1769176, 1779177, 1789178, 1791016, 1791106, 1791205,
1791304, 1791403, 1791502, 1791601, 1792015, 1793014, 1794013, 1795012,
1796011, 1803921, 1804922, 1805923, 1806924, 1807925, 1808926, 1819181,
1829182, 1839183, 1849184, 1859185, 1869186, 1879187, 1889188, 1891017,
1891107, 1891206, 1891305, 1891404, 1891503, 1891602, 1891701, 1892016, 1893015,
1894014, 1895013, 1896012, 1897011, 1919191, 2010194, 2010295, 2010396,
2010497, 2010598, 2011913, 2012914, 2013915, 2014916, 2015917, 2016918,
2019102, 2019201, 2019393, 2020195, 2020296, 2020397, 2020498, 2021923,
2022924, 2023925, 2024926, 2025927, 2026928, 2029103, 2029202, 2029301,
2029494, 2030196, 2030297, 2030398, 2031933, 2032934, 2033935, 2034936,
2035937, 2036938, 2039104, 2039203, 2039302, 2039401, 2039595, 2040197,
2040298, 2041943, 2042944, 2043945, 2044946, 2045947, 2046948, 2049105, 2049204,
2049303, 2049402, 2049501, 2049696, 2050198, 2051953, 2052954, 2053955,
2054956, 2055957, 2056958, 2059106, 2059205, 2059304, 2059403, 2059502,
2059601, 2059797, 2061963, 2062964, 2063965, 2064966, 2065967, 2066968,
2069107, 2069206, 2069305, 2069404, 2069503, 2069602, 2069701, 2069898,
2071973, 2072974, 2073975, 2074976, 2075977, 2076978, 2079108, 2079207,
2079306, 2079405, 2079504, 2079603, 2079702, 2079801, 2081983, 2082984,
2083985, 2084986, 2085987, 2086988, 2089208, 2089307, 2089406, 2089505, 2089604,
2089703, 2089802, 2101922, 2102923, 2103924, 2104925, 2105926, 2106927,
2107928, 2119211, 2129212, 2139213, 2149214, 2159215, 2169216, 2179217,
2189218, 2191308, 2191407, 2191506, 2191605, 2191704, 2191803, 2193018,
2194017, 2195016, 2196015, 2197014, 2198013, 2201923, 2202924, 2203925,
2204926, 2205927, 2206928, 2219221, 2229222, 2239223, 2249224, 2259225,
2269226, 2279227, 2289228, 2291021, 2291408, 2291507, 2291606, 2291705,
2291804, 2292101, 2294018, 2295017, 2296016, 2297015, 2298014, 2301924, 2302925,
2303926, 2304927, 2305928, 2308931, 2319231, 2329232, 2339233, 2349234,
2359235, 2369236, 2379237, 2389238, 2391022, 2391508, 2391607, 2391706,
2391805, 2392021, 2392102, 2392201, 2395018, 2396017, 2397016, 2398015,
2401925, 2402926, 2403927, 2404928, 2407931, 2408932, 2419241, 2429242,
2439243, 2449244, 2459245, 2469246, 2479247, 2489248, 2491023, 2491608,
2491707, 2491806, 2492022, 2492103, 2492202, 2492301, 2493021, 2496018,
2497017, 2498016, 2501926, 2502927, 2503928, 2506931, 2507932, 2508933, 2519251,
2529252, 2539253, 2549254, 2559255, 2569256, 2579257, 2589258, 2591024,
2591708, 2591807, 2592023, 2592104, 2592203, 2592302, 2592401, 2593022,
2594021, 2597018, 2598017, 2601927, 2602928, 2605931, 2606932, 2607933,
2608934, 2619261, 2629262, 2639263, 2649264, 2659265, 2669266, 2679267,
2689268, 2691025, 2691808, 2692024, 2692105, 2692204, 2692303, 2692402,
2692501, 2693023, 2694022, 2695021, 2698018, 2701928, 2704931, 2705932,
2706933, 2707934, 2708935, 2719271, 2729272, 2739273, 2749274, 2759275, 2769276,
2779277, 2789278, 2791026, 2792025, 2792106, 2792205, 2792304, 2792403,
2792502, 2792601, 2793024, 2794023, 2795022, 2796021, 2803931, 2804932,
2805933, 2806934, 2807935, 2808936, 2819281, 2829282, 2839283, 2849284,
2859285, 2869286, 2879287, 2889288, 2891027, 2892026, 2892107, 2892206,
2892305, 2892404, 2892503, 2892602, 2892701, 2893025, 2894024, 2895023,
2896022, 2897021, 2910192, 2929101, 2929292, 3010195, 3010296, 3010397,
3010498, 3011914, 3012915, 3013916, 3014917, 3015918, 3018921, 3019103,
3019202, 3019301, 3019494, 3020196, 3020297, 3020398, 3021924, 3022925,
3023926, 3024927, 3025928, 3028931, 3029104, 3029203, 3029302, 3029401,
3029595, 3030197, 3030298, 3031934, 3032935, 3033936, 3034937, 3035938,
3038941, 3039105, 3039204, 3039303, 3039402, 3039501, 3039696, 3040198,
3041944, 3042945, 3043946, 3044947, 3045948, 3048951, 3049106, 3049205,
3049304, 3049403, 3049502, 3049601, 3049797, 3051954, 3052955, 3053956,
3054957, 3055958, 3058961, 3059107, 3059206, 3059305, 3059404, 3059503, 3059602,
3059701, 3059898, 3061964, 3062965, 3063966, 3064967, 3065968, 3068971,
3069108, 3069207, 3069306, 3069405, 3069504, 3069603, 3069702, 3069801,
3071974, 3072975, 3073976, 3074977, 3075978, 3078981, 3079208, 3079307,
3079406, 3079505, 3079604, 3079703, 3079802, 3081984, 3082985, 3083986,
3084987, 3085988, 3089308, 3089407, 3089506, 3089605, 3089704, 3089803,
3101932, 3102933, 3103934, 3104935, 3105936, 3106937, 3107938, 3119311,
3129312, 3139313, 3149314, 3159315, 3169316, 3179317, 3189318, 3192308, 3192407,
3192506, 3192605, 3192704, 3192803, 3193028, 3194027, 3195026, 3196025,
3197024, 3198023, 3201933, 3202934, 3203935, 3204936, 3205937, 3206938,
3219321, 3229322, 3239323, 3249324, 3259325, 3269326, 3279327, 3289328,
3291031, 3292408, 3292507, 3292606, 3292705, 3292804, 3293101, 3294028,
3295027, 3296026, 3297025, 3298024, 3301934, 3302935, 3303936, 3304937,
3305938, 3308941, 3319331, 3329332, 3339333, 3349334, 3359335, 3369336,
3379337, 3389338, 3391032, 3392031, 3392508, 3392607, 3392706, 3392805, 3393102,
3393201, 3395028, 3396027, 3397026, 3398025, 3401935, 3402936, 3403937,
3404938, 3407941, 3408942, 3419341, 3429342, 3439343, 3449344, 3459345,
3469346, 3479347, 3489348, 3491033, 3492032, 3492608, 3492707, 3492806,
3493031, 3493103, 3493202, 3493301, 3496028, 3497027, 3498026, 3501936,
3502937, 3503938, 3506941, 3507942, 3508943, 3519351, 3529352, 3539353,
3549354, 3559355, 3569356, 3579357, 3589358, 3591034, 3592033, 3592708,
3592807, 3593032, 3593104, 3593203, 3593302, 3593401, 3594031, 3597028, 3598027,
3601937, 3602938, 3605941, 3606942, 3607943, 3608944, 3619361, 3629362,
3639363, 3649364, 3659365, 3669366, 3679367, 3689368, 3691035, 3692034,
3692808, 3693033, 3693105, 3693204, 3693303, 3693402, 3693501, 3694032,
3695031, 3698028, 3701938, 3704941, 3705942, 3706943, 3707944, 3708945,
3719371, 3729372, 3739373, 3749374, 3759375, 3769376, 3779377, 3789378,
3791036, 3792035, 3793034, 3793106, 3793205, 3793304, 3793403, 3793502,
3793601, 3794033, 3795032, 3796031, 3803941, 3804942, 3805943, 3806944, 3807945,
3808946, 3819381, 3829382, 3839383, 3849384, 3859385, 3869386, 3879387,
3889388, 3891037, 3892036, 3893035, 3893107, 3893206, 3893305, 3893404,
3893503, 3893602, 3893701, 3894034, 3895033, 3896032, 3897031, 3910101,
3910293, 3920193, 3939102, 3939201, 3939393, 4010196, 4010297, 4010398,
4011915, 4012916, 4013917, 4014918, 4017921, 4018922, 4019104, 4019203,
4019302, 4019401, 4019595, 4020197, 4020298, 4021925, 4022926, 4023927,
4024928, 4027931, 4028932, 4029105, 4029204, 4029303, 4029402, 4029501, 4029696,
4030198, 4031935, 4032936, 4033937, 4034938, 4037941, 4038942, 4039106,
4039205, 4039304, 4039403, 4039502, 4039601, 4039797, 4041945, 4042946,
4043947, 4044948, 4047951, 4048952, 4049107, 4049206, 4049305, 4049404,
4049503, 4049602, 4049701, 4049898, 4051955, 4052956, 4053957, 4054958,
4057961, 4058962, 4059108, 4059207, 4059306, 4059405, 4059504, 4059603,
4059702, 4059801, 4061965, 4062966, 4063967, 4064968, 4067971, 4068972,
4069208, 4069307, 4069406, 4069505, 4069604, 4069703, 4069802, 4071975, 4072976,
4073977, 4074978, 4077981, 4078982, 4079308, 4079407, 4079506, 4079605,
4079704, 4079803, 4081985, 4082986, 4083987, 4084988, 4089408, 4089507,
4089606, 4089705, 4089804, 4101942, 4102943, 4103944, 4104945, 4105946,
4106947, 4107948, 4119411, 4129412, 4139413, 4149414, 4159415, 4169416,
4179417, 4189418, 4193038, 4193308, 4193407, 4193506, 4193605, 4193704,
4193803, 4194037, 4195036, 4196035, 4197034, 4198033, 4201943, 4202944,
4203945, 4204946, 4205947, 4206948, 4219421, 4229422, 4239423, 4249424, 4259425,
4269426, 4279427, 4289428, 4291041, 4293408, 4293507, 4293606, 4293705,
4293804, 4294038, 4294101, 4295037, 4296036, 4297035, 4298034, 4301944,
4302945, 4303946, 4304947, 4305948, 4308951, 4319431, 4329432, 4339433,
4349434, 4359435, 4369436, 4379437, 4389438, 4391042, 4392041, 4393508,
4393607, 4393706, 4393805, 4394102, 4394201, 4395038, 4396037, 4397036,
4398035, 4401945, 4402946, 4403947, 4404948, 4407951, 4408952, 4419441,
4429442, 4439443, 4449444, 4459445, 4469446, 4479447, 4489448, 4491043,
4492042, 4493041, 4493608, 4493707, 4493806, 4494103, 4494202, 4494301,
4496038, 4497037, 4498036, 4501946, 4502947, 4503948, 4506951, 4507952,
4508953, 4519451, 4529452, 4539453, 4549454, 4559455, 4569456, 4579457,
4589458, 4591044, 4592043, 4593042, 4593708, 4593807, 4594041, 4594104,
4594203, 4594302, 4594401, 4597038, 4598037, 4601947, 4602948, 4605951,
4606952, 4607953, 4608954, 4619461, 4629462, 4639463, 4649464, 4659465,
4669466, 4679467, 4689468, 4691045, 4692044, 4693043, 4693808, 4694042, 4694105,
4694204, 4694303, 4694402, 4694501, 4695041, 4698038, 4701948, 4704951,
4705952, 4706953, 4707954, 4708955, 4719471, 4729472, 4739473, 4749474,
4759475, 4769476, 4779477, 4789478, 4791046, 4792045, 4793044, 4794043,
4794106, 4794205, 4794304, 4794403, 4794502, 4794601, 4795042, 4796041,
4803951, 4804952, 4805953, 4806954, 4807955, 4808956, 4819481, 4829482,
4839483, 4849484, 4859485, 4869486, 4879487, 4889488, 4891047, 4892046,
4893045, 4894044, 4894107, 4894206, 4894305, 4894404, 4894503, 4894602, 4894701,
4895043, 4896042, 4897041, 4910102, 4910201, 4910394, 4920101, 4920294,
4930194, 4949103, 4949202, 4949301, 4949494, 5010197, 5010298, 5011916,
5012917, 5013918, 5016921, 5017922, 5018923, 5019105, 5019204, 5019303,
5019402, 5019501, 5019696, 5020198, 5021926, 5022927, 5023928, 5026931,
5027932, 5028933, 5029106, 5029205, 5029304, 5029403, 5029502, 5029601,
5029797, 5031936, 5032937, 5033938, 5036941, 5037942, 5038943, 5039107,
5039206, 5039305, 5039404, 5039503, 5039602, 5039701, 5039898, 5041946, 5042947,
5043948, 5046951, 5047952, 5048953, 5049108, 5049207, 5049306, 5049405,
5049504, 5049603, 5049702, 5049801, 5051956, 5052957, 5053958, 5056961,
5057962, 5058963, 5059208, 5059307, 5059406, 5059505, 5059604, 5059703,
5059802, 5061966, 5062967, 5063968, 5066971, 5067972, 5068973, 5069308,
5069407, 5069506, 5069605, 5069704, 5069803, 5071976, 5072977, 5073978,
5076981, 5077982, 5078983, 5079408, 5079507, 5079606, 5079705, 5079804,
5081986, 5082987, 5083988, 5089508, 5089607, 5089706, 5089805, 5101952, 5102953,
5103954, 5104955, 5105956, 5106957, 5107958, 5119511, 5129512, 5139513,
5149514, 5159515, 5169516, 5179517, 5189518, 5193048, 5194047, 5194308,
5194407, 5194506, 5194605, 5194704, 5194803, 5195046, 5196045, 5197044,
5198043, 5201953, 5202954, 5203955, 5204956, 5205957, 5206958, 5219521,
5229522, 5239523, 5249524, 5259525, 5269526, 5279527, 5289528, 5291051,
5294048, 5294408, 5294507, 5294606, 5294705, 5294804, 5295047, 5295101,
5296046, 5297045, 5298044, 5301954, 5302955, 5303956, 5304957, 5305958, 5308961,
5319531, 5329532, 5339533, 5349534, 5359535, 5369536, 5379537, 5389538,
5391052, 5392051, 5394508, 5394607, 5394706, 5394805, 5395048, 5395102,
5395201, 5396047, 5397046, 5398045, 5401955, 5402956, 5403957, 5404958,
5407961, 5408962, 5419541, 5429542, 5439543, 5449544, 5459545, 5469546,
5479547, 5489548, 5491053, 5492052, 5493051, 5494608, 5494707, 5494806,
5495103, 5495202, 5495301, 5496048, 5497047, 5498046, 5501956, 5502957,
5503958, 5506961, 5507962, 5508963, 5519551, 5529552, 5539553, 5549554, 5559555,
5569556, 5579557, 5589558, 5591054, 5592053, 5593052, 5594051, 5594708,
5594807, 5595104, 5595203, 5595302, 5595401, 5597048, 5598047, 5601957,
5602958, 5605961, 5606962, 5607963, 5608964, 5619561, 5629562, 5639563,
5649564, 5659565, 5669566, 5679567, 5689568, 5691055, 5692054, 5693053,
5694052, 5694808, 5695051, 5695105, 5695204, 5695303, 5695402, 5695501,
5698048, 5701958, 5704961, 5705962, 5706963, 5707964, 5708965, 5719571,
5729572, 5739573, 5749574, 5759575, 5769576, 5779577, 5789578, 5791056, 5792055,
5793054, 5794053, 5795052, 5795106, 5795205, 5795304, 5795403, 5795502,
5795601, 5796051, 5803961, 5804962, 5805963, 5806964, 5807965, 5808966,
5819581, 5829582, 5839583, 5849584, 5859585, 5869586, 5879587, 5889588,
5891057, 5892056, 5893055, 5894054, 5895053, 5895107, 5895206, 5895305,
5895404, 5895503, 5895602, 5895701, 5896052, 5897051, 5910103, 5910202,
5910301, 5910495, 5920102, 5920201, 5920395, 5930101, 5930295, 5940195,
5959104, 5959203, 5959302, 5959401, 5959595, 6010198, 6011917, 6012918, 6015921,
6016922, 6017923, 6018924, 6019106, 6019205, 6019304, 6019403, 6019502,
6019601, 6019797, 6021927, 6022928, 6025931, 6026932, 6027933, 6028934,
6029107, 6029206, 6029305, 6029404, 6029503, 6029602, 6029701, 6029898,
6031937, 6032938, 6035941, 6036942, 6037943, 6038944, 6039108, 6039207,
6039306, 6039405, 6039504, 6039603, 6039702, 6039801, 6041947, 6042948,
6045951, 6046952, 6047953, 6048954, 6049208, 6049307, 6049406, 6049505,
6049604, 6049703, 6049802, 6051957, 6052958, 6055961, 6056962, 6057963,
6058964, 6059308, 6059407, 6059506, 6059605, 6059704, 6059803, 6061967,
6062968, 6065971, 6066972, 6067973, 6068974, 6069408, 6069507, 6069606,
6069705, 6069804, 6071977, 6072978, 6075981, 6076982, 6077983, 6078984,
6079508, 6079607, 6079706, 6079805, 6081987, 6082988, 6089608, 6089707,
6089806, 6101962, 6102963, 6103964, 6104965, 6105966, 6106967, 6107968,
6119611, 6129612, 6139613, 6149614, 6159615, 6169616, 6179617, 6189618,
6193058, 6194057, 6195056, 6195308, 6195407, 6195506, 6195605, 6195704, 6195803,
6196055, 6197054, 6198053, 6201963, 6202964, 6203965, 6204966, 6205967,
6206968, 6219621, 6229622, 6239623, 6249624, 6259625, 6269626, 6279627,
6289628, 6291061, 6294058, 6295057, 6295408, 6295507, 6295606, 6295705,
6295804, 6296056, 6296101, 6297055, 6298054, 6301964, 6302965, 6303966,
6304967, 6305968, 6308971, 6319631, 6329632, 6339633, 6349634, 6359635,
6369636, 6379637, 6389638, 6391062, 6392061, 6395058, 6395508, 6395607,
6395706, 6395805, 6396057, 6396102, 6396201, 6397056, 6398055, 6401965, 6402966,
6403967, 6404968, 6407971, 6408972, 6419641, 6429642, 6439643, 6449644,
6459645, 6469646, 6479647, 6489648, 6491063, 6492062, 6493061, 6495608,
6495707, 6495806, 6496058, 6496103, 6496202, 6496301, 6497057, 6498056,
6501966, 6502967, 6503968, 6506971, 6507972, 6508973, 6519651, 6529652,
6539653, 6549654, 6559655, 6569656, 6579657, 6589658, 6591064, 6592063,
6593062, 6594061, 6595708, 6595807, 6596104, 6596203, 6596302, 6596401,
6597058, 6598057, 6601967, 6602968, 6605971, 6606972, 6607973, 6608974, 6619661,
6629662, 6639663, 6649664, 6659665, 6669666, 6679667, 6689668, 6691065,
6692064, 6693063, 6694062, 6695061, 6695808, 6696105, 6696204, 6696303,
6696402, 6696501, 6698058, 6701968, 6704971, 6705972, 6706973, 6707974,
6708975, 6719671, 6729672, 6739673, 6749674, 6759675, 6769676, 6779677,
6789678, 6791066, 6792065, 6793064, 6794063, 6795062, 6796061, 6796106,
6796205, 6796304, 6796403, 6796502, 6796601, 6803971, 6804972, 6805973,
6806974, 6807975, 6808976, 6819681, 6829682, 6839683, 6849684, 6859685, 6869686,
6879687, 6889688, 6891067, 6892066, 6893065, 6894064, 6895063, 6896062,
6896107, 6896206, 6896305, 6896404, 6896503, 6896602, 6896701, 6897061,
6910104, 6910203, 6910302, 6910401, 6910596, 6920103, 6920202, 6920301,
6920496, 6930102, 6930201, 6930396, 6940101, 6940296, 6950196, 6969105,
6969204, 6969303, 6969402, 6969501, 6969696, 7011918, 7014921, 7015922,
7016923, 7017924, 7018925, 7019107, 7019206, 7019305, 7019404, 7019503,
7019602, 7019701, 7019898, 7021928, 7024931, 7025932, 7026933, 7027934, 7028935,
7029108, 7029207, 7029306, 7029405, 7029504, 7029603, 7029702, 7029801,
7031938, 7034941, 7035942, 7036943, 7037944, 7038945, 7039208, 7039307,
7039406, 7039505, 7039604, 7039703, 7039802, 7041948, 7044951, 7045952,
7046953, 7047954, 7048955, 7049308, 7049407, 7049506, 7049605, 7049704,
7049803, 7051958, 7054961, 7055962, 7056963, 7057964, 7058965, 7059408,
7059507, 7059606, 7059705, 7059804, 7061968, 7064971, 7065972, 7066973,
7067974, 7068975, 7069508, 7069607, 7069706, 7069805, 7071978, 7074981, 7075982,
7076983, 7077984, 7078985, 7079608, 7079707, 7079806, 7081988, 7089708,
7089807, 7101972, 7102973, 7103974, 7104975, 7105976, 7106977, 7107978,
7119711, 7129712, 7139713, 7149714, 7159715, 7169716, 7179717, 7189718,
7193068, 7194067, 7195066, 7196065, 7196308, 7196407, 7196506, 7196605,
7196704, 7196803, 7197064, 7198063, 7201973, 7202974, 7203975, 7204976,
7205977, 7206978, 7219721, 7229722, 7239723, 7249724, 7259725, 7269726,
7279727, 7289728, 7291071, 7294068, 7295067, 7296066, 7296408, 7296507, 7296606,
7296705, 7296804, 7297065, 7297101, 7298064, 7301974, 7302975, 7303976,
7304977, 7305978, 7308981, 7319731, 7329732, 7339733, 7349734, 7359735,
7369736, 7379737, 7389738, 7391072, 7392071, 7395068, 7396067, 7396508,
7396607, 7396706, 7396805, 7397066, 7397102, 7397201, 7398065, 7401975,
7402976, 7403977, 7404978, 7407981, 7408982, 7419741, 7429742, 7439743,
7449744, 7459745, 7469746, 7479747, 7489748, 7491073, 7492072, 7493071,
7496068, 7496608, 7496707, 7496806, 7497067, 7497103, 7497202, 7497301, 7498066,
7501976, 7502977, 7503978, 7506981, 7507982, 7508983, 7519751, 7529752,
7539753, 7549754, 7559755, 7569756, 7579757, 7589758, 7591074, 7592073,
7593072, 7594071, 7596708, 7596807, 7597068, 7597104, 7597203, 7597302,
7597401, 7598067, 7601977, 7602978, 7605981, 7606982, 7607983, 7608984,
7619761, 7629762, 7639763, 7649764, 7659765, 7669766, 7679767, 7689768,
7691075, 7692074, 7693073, 7694072, 7695071, 7696808, 7697105, 7697204,
7697303, 7697402, 7697501, 7698068, 7701978, 7704981, 7705982, 7706983,
7707984, 7708985, 7719771, 7729772, 7739773, 7749774, 7759775, 7769776,
7779777, 7789778, 7791076, 7792075, 7793074, 7794073, 7795072, 7796071,
7797106, 7797205, 7797304, 7797403, 7797502, 7797601, 7803981, 7804982,
7805983, 7806984, 7807985, 7808986, 7819781, 7829782, 7839783, 7849784,
7859785, 7869786, 7879787, 7889788, 7891077, 7892076, 7893075, 7894074,
7895073, 7896072, 7897071, 7897107, 7897206, 7897305, 7897404, 7897503,
7897602, 7897701, 7910105, 7910204, 7910303, 7910402, 7910501, 7910697, 7920104,
7920203, 7920302, 7920401, 7920597, 7930103, 7930202, 7930301, 7930497,
7940102, 7940201, 7940397, 7950101, 7950297, 7960197, 7979106, 7979205,
7979304, 7979403, 7979502, 7979601, 7979797, 8013921, 8014922, 8015923,
8016924, 8017925, 8018926, 8019108, 8019207, 8019306, 8019405, 8019504,
8019603, 8019702, 8019801, 8023931, 8024932, 8025933, 8026934, 8027935,
8028936, 8029208, 8029307, 8029406, 8029505, 8029604, 8029703, 8029802,
8033941, 8034942, 8035943, 8036944, 8037945, 8038946, 8039308, 8039407, 8039506,
8039605, 8039704, 8039803, 8043951, 8044952, 8045953, 8046954, 8047955,
8048956, 8049408, 8049507, 8049606, 8049705, 8049804, 8053961, 8054962,
8055963, 8056964, 8057965, 8058966, 8059508, 8059607, 8059706, 8059805,
8063971, 8064972, 8065973, 8066974, 8067975, 8068976, 8069608, 8069707,
8069806, 8073981, 8074982, 8075983, 8076984, 8077985, 8078986, 8079708,
8079807, 8089808, 8101982, 8102983, 8103984, 8104985, 8105986, 8106987,
8107988, 8119811, 8129812, 8139813, 8149814, 8159815, 8169816, 8179817, 8189818,
8193078, 8194077, 8195076, 8196075, 8197074, 8197308, 8197407, 8197506,
8197605, 8197704, 8197803, 8198073, 8201983, 8202984, 8203985, 8204986,
8205987, 8206988, 8219821, 8229822, 8239823, 8249824, 8259825, 8269826,
8279827, 8289828, 8291081, 8294078, 8295077, 8296076, 8297075, 8297408,
8297507, 8297606, 8297705, 8297804, 8298074, 8298101, 8301984, 8302985,
8303986, 8304987, 8305988, 8319831, 8329832, 8339833, 8349834, 8359835,
8369836, 8379837, 8389838, 8391082, 8392081, 8395078, 8396077, 8397076, 8397508,
8397607, 8397706, 8397805, 8398075, 8398102, 8398201, 8401985, 8402986,
8403987, 8404988, 8419841, 8429842, 8439843, 8449844, 8459845, 8469846,
8479847, 8489848, 8491083, 8492082, 8493081, 8496078, 8497077, 8497608,
8497707, 8497806, 8498076, 8498103, 8498202, 8498301, 8501986, 8502987,
8503988, 8519851, 8529852, 8539853, 8549854, 8559855, 8569856, 8579857,
8589858, 8591084, 8592083, 8593082, 8594081, 8597078, 8597708, 8597807,
8598077, 8598104, 8598203, 8598302, 8598401, 8601987, 8602988, 8619861, 8629862,
8639863, 8649864, 8659865, 8669866, 8679867, 8689868, 8691085, 8692084,
8693083, 8694082, 8695081, 8697808, 8698078, 8698105, 8698204, 8698303,
8698402, 8698501, 8701988, 8719871, 8729872, 8739873, 8749874, 8759875,
8769876, 8779877, 8789878, 8791086, 8792085, 8793084, 8794083, 8795082,
8796081, 8798106, 8798205, 8798304, 8798403, 8798502, 8798601, 8819881,
8829882, 8839883, 8849884, 8859885, 8869886, 8879887, 8889888, 8891087,
8892086, 8893085, 8894084, 8895083, 8896082, 8897081, 8898107, 8898206, 8898305,
8898404, 8898503, 8898602, 8898701, 8910106, 8910205, 8910304, 8910403,
8910502, 8910601, 8910798, 8920105, 8920204, 8920303, 8920402, 8920501,
8920698, 8930104, 8930203, 8930302, 8930401, 8930598, 8940103, 8940202,
8940301, 8940498, 8950102, 8950201, 8950398, 8960101, 8960298, 8970198,
8989107, 8989206, 8989305, 8989404, 8989503, 8989602, 8989701, 8989898.
Number
of 8-digit solutions:
=\+ 0
1 2 3
4 5 6
7 8
1 1898
2 2766
868
3 3010
1246 2060
4 3118
1404 2182 2402
5 3080
1394 2230 2500
2418
6 3204
1492 2328 2418
2490 2384
7 3294
1588 2386 2438
2532 2564 2556
8 3376 1590 2384
2558 2558 2640
2680 2720
9 3366 1446
2304 2470 2534
2564 2644 2726
2704
Hans H.: « A bit of a surprise here:
[0+;8=] beats [0+;9=] with ten more solutions. Since they were so
close, I've listed both sets, side by side, in the attachment. I thought there might
be an easy way to list them
with the ten
"extra" solutions in [0+;8=] left empty in [0+;9=], instead of all ten at the end of the list. However, it doesn't appear
to be a trivial problem to
figure out what the ten
extra solutions are, in a side-by-side
comparison - or, at least I
didn't see it in a cursory examination. »
Maximum (3376) & Runner-Up (3366):
1 1+1+9=11
1+11=4+8
2 1+11=3+9
1+11=5+7
3 1+11=5+7
1+11=6+6
4 1+11=6+6
1+11=7+5
5 1+11=7+5
1+11=8+4
6 1+11=9+3
1+12=5+8
7 1+12=4+9
1+12=6+7
8 1+12=6+7
1+12=7+6
9 1+12=7+6
1+12=8+5
10 1+12=9+4
1+13=6+8
11 1+13=5+9
1+13=7+7
12 1+13=7+7
1+13=8+6
13 1+13=9+5
1+14=7+8
14 1+14=6+9
1+14=8+7
15 1+14=9+6
1+15=8+8
16 1+15=7+9
1+2+8=11
17 1+15=9+7
1+3+7=11
18 1+17=9+9
1+3+8=12
19 1+2+9=12
1+4+6=11
20 1+3+7=11
1+4+7=12
21 1+3+9=13
1+4+8=13
22 1+4+6=11
1+5+5=11
23 1+4+7=12
1+5+6=12
24 1+4+9=14
1+5+7=13
25 1+5+5=11
1+5+8=14
26 1+5+6=12
1+6+4=11
27 1+5+7=13
1+6+5=12
28 1+5+9=15
1+6+6=13
29 1+6+4=11
1+6+7=14
30 1+6+5=12
1+6+8=15
31 1+6+6=13
1+7+3=11
32 1+6+7=14
1+7+4=12
33 1+6+9=16
1+7+5=13
34 1+7+3=11
1+7+6=14
35 1+7+4=12
1+7+7=15
36 1+7+5=13
1+7+8=16
37 1+7+6=14
1+8+2=11
38 1+7+7=15
1+8+3=12
39 1+7+9=17
1+8+4=13
40 1+9+1=11
1+8+5=14
41 1+9+2=12
1+8+6=15
42 1+9+3=13
1+8+7=16
43 1+9+4=14
1+8+8=17
44 1+9+5=15
11+11=22
45 1+9+6=16
11+12=23
46 1+9+7=17
11+13=24
47 1+9+9=19
11+14=25
48 11+11=22
11+15=26
49 11+12=23
11+16=27
50 11+13=24
11+17=28
51 11+14=25
11+1=4+8
52 11+15=26
11+1=5+7
53 11+16=27
11+1=6+6
54 11+1=3+9
11+1=7+5
55 11+1=5+7
11+1=8+4
56 11+1=6+6
11+21=32
57 11+1=7+5
11+22=33
58 11+1=9+3
11+23=34
59 11+21=32
11+24=35
60 11+22=33
11+25=36
61 11+23=34
11+26=37
62 11+24=35
11+27=38
63 11+25=36
11+2=5+8
64 11+26=37
11+2=6+7
65 11+2=4+9
11+2=7+6
66 11+2=6+7
11+2=8+5
67 11+2=7+6
11+31=42
68 11+2=9+4
11+32=43
69 11+31=42
11+33=44
70 11+32=43
11+34=45
71 11+33=44
11+35=46
72 11+34=45
11+36=47
73 11+35=46
11+37=48
74 11+36=47
11+3=6+8
75 11+3=5+9
11+3=7+7
76 11+3=7+7
11+3=8+6
77 11+3=9+5
11+41=52
78 11+41=52
11+42=53
79 11+42=53
11+43=54
80 11+43=54
11+44=55
81 11+44=55
11+45=56
82 11+45=56
11+46=57
83 11+46=57
11+47=58
84 11+4=6+9
11+4=7+8
85 11+4=9+6
11+4=8+7
86 11+51=62 11+51=62
87 11+52=63 11+52=63
88 11+53=64 11+53=64
89 11+54=65 11+54=65
90 11+55=66 11+55=66
91 11+56=67 11+56=67
92 11+5=7+9
11+57=68
93 11+5=9+7
11+5=8+8
94 11+61=72 11+61=72
95 11+62=73 11+62=73
96 11+63=74 11+63=74
97 11+64=75 11+64=75
98 11+65=76 11+65=76
99 11+66=77 11+66=77
100 11+7=9+9
11+67=78
101 11=1+1+9
11+71=82
102 11=1+3+7
11+72=83
103 11=1+4+6
11+73=84
104 11=1+5+5
11+74=85
105 11=1+6+4
11+75=86
106 11=1+7+3
11+76=87
107 11=1+9+1
11+77=88
108 11=11=11
11=1+2+8
109 11=2+2+7
11=1+3+7
110 11=2+3+6
11=1+4+6
111 11=2+4+5
11=1+5+5
112 11=2+5+4
11=1+6+4
113 11=2+6+3
11=1+7+3
114 11=2+7+2
11=1+8+2
115 11=3+1+7
11=11=11
116 11=3+2+6
11=2+1+8
117 11=3+3+5
11=2+2+7
118 11=3+4+4
11=2+3+6
119 11=3+5+3
11=2+4+5
120 11=3+6+2
11=2+5+4
121 11=3+7+1
11=2+6+3
122 11=4+1+6
11=2+7+2
123 11=4+2+5
11=2+8+1
124 11=4+3+4
11=3+1+7
125 11=4+4+3
11=3+2+6
126 11=4+5+2
11=3+3+5
127 11=4+6+1
11=3+4+4
128 11=5+1+5
11=3+5+3
129 11=5+2+4
11=3+6+2
130 11=5+3+3
11=3+7+1
131 11=5+4+2
11=4+1+6
132 11=5+5+1
11=4+2+5
133 11=6+1+4
11=4+3+4
134 11=6+2+3
11=4+4+3
135 11=6+3+2
11=4+5+2
136 11=6+4+1
11=4+6+1
137 11=7+1+3
11=5+1+5
138 11=7+2+2
11=5+2+4
139 11=7+3+1
11=5+3+3
140 11=9+1+1
11=5+4+2
141 12+11=23
11=5+5+1
142 12+12=24
11=6+1+4
143 12+13=25
11=6+2+3
144 12+14=26
11=6+3+2
145 12+15=27
11=6+4+1
146 12+17=29
11=7+1+3
147 12+1=4+9
11=7+2+2
148 12+1=6+7
11=7+3+1
149 12+1=7+6
11=8+1+2
150 12+1=9+4
11=8+2+1
151 12+19=31
12+11=23
152 12+21=33
12+12=24
153 12+22=34
12+13=25
154 12+23=35
12+14=26
155 12+24=36
12+15=27
156 12+25=37
12+16=28
157 12+27=39
12+1=5+8
158 12+2=5+9
12+1=6+7
159 12+2=7+7
12+1=7+6
160 12+2=9+5
12+1=8+5
161 12+29=41
12+21=33
162 12+31=43
12+22=34
163 12+32=44
12+23=35
164 12+33=45
12+24=36
165 12+34=46
12+25=37
166 12+35=47
12+26=38
167 12+37=49
12+2=6+8
168 12+3=6+9
12+2=7+7
169 12+3=9+6
12+2=8+6
170 12+39=51
12+31=43
171 12+41=53
12+32=44
172 12+42=54
12+33=45
173 12+43=55
12+34=46
174 12+44=56
12+35=47
175 12+45=57
12+36=48
176 12+47=59
12+3=7+8
177 12+4=7+9
12+3=8+7
178 12+4=9+7
12+41=53
179 12+49=61
12+42=54
180 12+51=63
12+43=55
181 12+52=64
12+44=56
182 12+53=65
12+45=57
183 12+54=66
12+46=58
184 12+55=67
12+4=8+8
185 12+57=69
12+51=63
186 12+59=71
12+52=64
187 12+61=73
12+53=65
188 12+62=74
12+54=66
189 12+63=75
12+55=67
190 12+64=76
12+56=68
191 12+65=77
12+61=73
192 12+67=79
12+62=74
193 12+6=9+9
12+63=75
194 12+79=91
12+64=76
195 12=1+2+9
12+65=77
196 12=1+4+7
12+66=78
197 12=1+5+6
12+71=83
198 12=1+6+5
12+72=84
199 12=1+7+4
12+73=85
200 12=1+9+2
12+74=86
201 12=12=12
12+75=87
202 12=2+1+9
12+76=88
203 12=2+3+7
12=1+3+8
204 12=2+4+6
12=1+4+7
205 12=2+5+5
12=1+5+6
206 12=2+6+4
12=1+6+5
207 12=2+7+3
12=1+7+4
208 12=2+9+1
12=1+8+3
209 12=3+2+7
12=12=12
210 12=3+3+6
12=2+2+8
211 12=3+4+5
12=2+3+7
212 12=3+5+4
12=2+4+6
213 12=3+6+3
12=2+5+5
214 12=3+7+2
12=2+6+4
215 12=4+1+7
12=2+7+3
216 12=4+2+6
12=2+8+2
217 12=4+3+5
12=3+1+8
218 12=4+4+4
12=3+2+7
219 12=4+5+3
12=3+3+6
220 12=4+6+2
12=3+4+5
221 12=4+7+1
12=3+5+4
222 12=5+1+6
12=3+6+3
223 12=5+2+5
12=3+7+2
224 12=5+3+4
12=3+8+1
225 12=5+4+3
12=4+1+7
226 12=5+5+2
12=4+2+6
227 12=5+6+1
12=4+3+5
228 12=6+1+5
12=4+4+4
229 12=6+2+4
12=4+5+3
230 12=6+3+3
12=4+6+2
231 12=6+4+2
12=4+7+1
232 12=6+5+1
12=5+1+6
233 12=7+1+4
12=5+2+5
234 12=7+2+3
12=5+3+4
235 12=7+3+2
12=5+4+3
236 12=7+4+1
12=5+5+2
237 12=9+1+2
12=5+6+1
238 12=9+2+1
12=6+1+5
239 13+11=24
12=6+2+4
240 13+12=25
12=6+3+3
241 13+13=26
12=6+4+2
242 13+14=27
12=6+5+1
243 13+16=29
12=7+1+4
244 13+1=5+9
12=7+2+3
245 13+1=7+7
12=7+3+2
246 13+1=9+5
12=7+4+1
247 13+19=32
12=8+1+3
248 13+21=34
12=8+2+2
249 13+22=35
12=8+3+1
250 13+23=36
13+11=24
251 13+24=37
13+12=25
252 13+26=39
13+13=26
253 13+2=6+9
13+14=27
254 13+2=9+6
13+15=28
255 13+29=42
13+18=31
256 13+31=44
13+1=6+8
257 13+32=45
13+1=7+7
258 13+33=46
13+1=8+6
259 13+34=47
13+21=34
260 13+36=49
13+22=35
261 13+3=7+9
13+23=36
262 13+3=9+7
13+24=37
263 13+39=52
13+25=38
264 13+41=54
13+28=41
265 13+42=55
13+2=7+8
266 13+43=56
13+2=8+7
267 13+44=57
13+31=44
268 13+46=59
13+32=45
269 13+49=62
13+33=46
270 13+51=64
13+34=47
271 13+52=65
13+35=48
272 13+53=66
13+38=51
273 13+54=67
13+3=8+8
274 13+56=69
13+41=54
275 13+5=9+9
13+42=55
276 13+59=72
13+43=56
277 13+61=74
13+44=57
278 13+62=75
13+45=58
279 13+63=76
13+48=61
280 13+64=77
13+51=64
281 13+66=79
13+52=65
282 13+79=92
13+53=66
283 13=1+3+9
13+54=67
284 13=1+5+7
13+55=68
285 13=1+6+6
13+58=71
286 13=1+7+5
13+61=74
287 13=1+9+3
13+62=75
288 13=13=13
13+63=76
289 13=2+2+9
13+64=77
290 13=2+4+7
13+65=78
291 13=2+5+6
13+68=81
292 13=2+6+5
13+71=84
293 13=2+7+4
13+72=85
294 13=2+9+2
13+73=86
295 13=3+1+9
13+74=87
296 13=3+3+7
13+75=88
297 13=3+4+6
13=1+4+8
298 13=3+5+5
13=1+5+7
299 13=3+6+4
13=1+6+6
300 13=3+7+3
13=1+7+5
301 13=3+9+1
13=1+8+4
302 13=4+2+7
13=13=13
303 13=4+3+6
13=2+3+8
304 13=4+4+5
13=2+4+7
305 13=4+5+4
13=2+5+6
306 13=4+6+3
13=2+6+5
307 13=4+7+2
13=2+7+4
308 13=5+1+7
13=2+8+3
309 13=5+2+6
13=3+2+8
310 13=5+3+5
13=3+3+7
311 13=5+4+4
13=3+4+6
312 13=5+5+3
13=3+5+5
313 13=5+6+2
13=3+6+4
314 13=5+7+1
13=3+7+3
315 13=6+1+6
13=3+8+2
316 13=6+2+5
13=4+1+8
317 13=6+3+4
13=4+2+7
318 13=6+4+3
13=4+3+6
319 13=6+5+2
13=4+4+5
320 13=6+6+1
13=4+5+4
321 13=7+1+5
13=4+6+3
322 13=7+2+4
13=4+7+2
323 13=7+3+3
13=4+8+1
324 13=7+4+2
13=5+1+7
325 13=7+5+1
13=5+2+6
326 13=9+1+3
13=5+3+5
327 13=9+2+2
13=5+4+4
328 13=9+3+1
13=5+5+3
329 14+11=25
13=5+6+2
330 14+12=26
13=5+7+1
331 14+13=27
13=6+1+6
332 14+15=29
13=6+2+5
333 14+17=31
13=6+3+4
334 14+1=6+9
13=6+4+3
335 14+1=9+6
13=6+5+2
336 14+19=33
13=6+6+1
337 14+21=35
13=7+1+5
338 14+22=36
13=7+2+4
339 14+23=37
13=7+3+3
340 14+25=39
13=7+4+2
341 14+27=41
13=7+5+1
342 14+2=7+9
13=8+1+4
343 14+2=9+7
13=8+2+3
344 14+29=43
13=8+3+2
345 14+31=45
13=8+4+1
346 14+32=46
14+11=25
347 14+33=47
14+12=26
348 14+35=49
14+13=27
349 14+37=51
14+14=28
350 14+39=53
14+17=31
351 14+41=55
14+18=32
352 14+42=56
14+1=7+8
353 14+43=57
14+1=8+7
354 14+45=59
14+21=35
355 14+47=61
14+22=36
356 14+4=9+9
14+23=37
357 14+49=63
14+24=38
358 14+51=65
14+27=41
359 14+52=66
14+28=42
360 14+53=67
14+2=8+8
361 14+55=69
14+31=45
362 14+57=71
14+32=46
363 14+59=73
14+33=47
364 14+61=75
14+34=48
365 14+62=76
14+37=51
366 14+63=77
14+38=52
367 14+65=79
14+41=55
368 14+77=91
14+42=56
369 14+79=93
14+43=57
370 14=1+4+9
14+44=58
371 14=1+6+7
14+47=61
372 14=1+7+6
14+48=62
373 14=1+9+4
14+51=65
374 14=14=14
14+52=66
375 14=2+3+9
14+53=67
376 14=2+5+7
14+54=68
377 14=2+6+6
14+57=71
378 14=2+7+5
14+58=72
379 14=2+9+3
14+61=75
380 14=3+2+9
14+62=76
381 14=3+4+7
14+63=77
382 14=3+5+6
14+64=78
383 14=3+6+5
14+67=81
384 14=3+7+4
14+68=82
385 14=3+9+2
14+71=85
386 14=4+1+9
14+72=86
387 14=4+3+7
14+73=87
388 14=4+4+6
14+74=88
389 14=4+5+5
14=1+5+8
390 14=4+6+4
14=1+6+7
391 14=4+7+3
14=1+7+6
392 14=4+9+1
14=1+8+5
393 14=5+2+7
14=14=14
394 14=5+3+6
14=2+4+8
395 14=5+4+5
14=2+5+7
396 14=5+5+4
14=2+6+6
397 14=5+6+3
14=2+7+5
398 14=5+7+2
14=2+8+4
399 14=6+1+7
14=3+3+8
400 14=6+2+6
14=3+4+7
401 14=6+3+5
14=3+5+6
402 14=6+4+4
14=3+6+5
403 14=6+5+3
14=3+7+4
404 14=6+6+2
14=3+8+3
405 14=6+7+1
14=4+2+8
406 14=7+1+6
14=4+3+7
407 14=7+2+5
14=4+4+6
408 14=7+3+4
14=4+5+5
409 14=7+4+3
14=4+6+4
410 14=7+5+2
14=4+7+3
411 14=7+6+1
14=4+8+2
412 14=9+1+4
14=5+1+8
413 14=9+2+3
14=5+2+7
414 14=9+3+2
14=5+3+6
415 14=9+4+1
14=5+4+5
416 15+11=26
14=5+5+4
417 15+12=27
14=5+6+3
418 15+14=29
14=5+7+2
419 15+16=31
14=5+8+1
420 15+17=32
14=6+1+7
421 15+1=7+9
14=6+2+6
422 15+1=9+7
14=6+3+5
423 15+19=34
14=6+4+4
424 15+21=36
14=6+5+3
425 15+22=37
14=6+6+2
426 15+24=39
14=6+7+1
427 15+26=41
14=7+1+6
428 15+27=42
14=7+2+5
429 15+29=44
14=7+3+4
430 15+31=46
14=7+4+3
431 15+32=47
14=7+5+2
432 15+34=49
14=7+6+1
433 15+36=51
14=8+1+5
434 15+37=52
14=8+2+4
435 15+3=9+9
14=8+3+3
436 15+39=54
14=8+4+2
437 15+41=56
14=8+5+1
438 15+42=57
15+11=26
439 15+44=59
15+12=27
440 15+46=61
15+13=28
441 15+47=62
15+16=31
442 15+49=64
15+17=32
443 15+51=66
15+18=33
444 15+52=67
15+1=8+8
445 15+54=69
15+21=36
446 15+56=71
15+22=37
447 15+57=72
15+23=38
448 15+59=74
15+26=41
449 15+61=76
15+27=42
450 15+62=77
15+28=43
451 15+64=79
15+31=46
452 15+76=91
15+32=47
453 15+77=92
15+33=48
454 15+79=94
15+36=51
455 15=1+5+9
15+37=52
456 15=1+7+7
15+38=53
457 15=1+9+5
15+41=56
458 15=15=15
15+42=57
459 15=2+4+9
15+43=58
460 15=2+6+7
15+46=61
461 15=2+7+6
15+47=62
462 15=2+9+4
15+48=63
463 15=3+3+9
15+51=66
464 15=3+5+7
15+52=67
465 15=3+6+6
15+53=68
466 15=3+7+5
15+56=71
467 15=3+9+3
15+57=72
468 15=4+2+9
15+58=73
469 15=4+4+7
15+61=76
470 15=4+5+6
15+62=77
471 15=4+6+5
15+63=78
472 15=4+7+4
15+66=81
473 15=4+9+2
15+67=82
474 15=5+1+9
15+68=83
475 15=5+3+7
15+71=86
476 15=5+4+6
15+72=87
477 15=5+5+5
15+73=88
478 15=5+6+4
15=1+6+8
479 15=5+7+3
15=1+7+7
480 15=5+9+1
15=1+8+6
481 15=6+2+7
15=15=15
482 15=6+3+6
15=2+5+8
483 15=6+4+5
15=2+6+7
484 15=6+5+4
15=2+7+6
485 15=6+6+3
15=2+8+5
486 15=6+7+2
15=3+4+8
487 15=7+1+7
15=3+5+7
488 15=7+2+6
15=3+6+6
489 15=7+3+5
15=3+7+5
490 15=7+4+4
15=3+8+4
491 15=7+5+3
15=4+3+8
492 15=7+6+2
15=4+4+7
493 15=7+7+1
15=4+5+6
494 15=9+1+5
15=4+6+5
495 15=9+2+4
15=4+7+4
496 15=9+3+3
15=4+8+3
497 15=9+4+2
15=5+2+8
498 15=9+5+1
15=5+3+7
499 16+11=27
15=5+4+6
500 16+13=29
15=5+5+5
501 16+15=31
15=5+6+4
502 16+16=32
15=5+7+3
503 16+17=33
15=5+8+2
504 16+19=35
15=6+1+8
505 16+21=37
15=6+2+7
506 16+23=39
15=6+3+6
507 16+25=41
15=6+4+5
508 16+26=42
15=6+5+4
509 16+27=43
15=6+6+3
510 16+2=9+9
15=6+7+2
511 16+29=45
15=6+8+1
512 16+31=47
15=7+1+7
513 16+33=49
15=7+2+6
514 16+35=51
15=7+3+5
515 16+36=52
15=7+4+4
516 16+37=53
15=7+5+3
517 16+39=55
15=7+6+2
518 16+41=57
15=7+7+1
519 16+43=59
15=8+1+6
520 16+45=61
15=8+2+5
521 16+46=62
15=8+3+4
522 16+47=63
15=8+4+3
523 16+49=65
15=8+5+2
524 16+51=67
15=8+6+1
525 16+53=69
16+11=27
526 16+55=71
16+12=28
527 16+56=72
16+15=31
528 16+57=73
16+16=32
529 16+59=75
16+17=33
530 16+61=77
16+18=34
531 16+63=79
16+21=37
532 16+75=91
16+22=38
533 16+76=92
16+25=41
534 16+77=93
16+26=42
535 16+79=95
16+27=43
536 16=1+6+9
16+28=44
537 16=1+9+6
16+31=47
538 16=16=16
16+32=48
539 16=2+5+9
16+35=51
540 16=2+7+7
16+36=52
541 16=2+9+5
16+37=53
542 16=3+4+9
16+38=54
543 16=3+6+7
16+41=57
544 16=3+7+6
16+42=58
545 16=3+9+4
16+45=61
546 16=4+3+9
16+46=62
547 16=4+5+7
16+47=63
548 16=4+6+6
16+48=64
549 16=4+7+5
16+51=67
550 16=4+9+3
16+52=68
551 16=5+2+9
16+55=71
552 16=5+4+7
16+56=72
553 16=5+5+6
16+57=73
554 16=5+6+5
16+58=74
555 16=5+7+4
16+61=77
556 16=5+9+2
16+62=78
557 16=6+1+9
16+65=81
558 16=6+3+7
16+66=82
559 16=6+4+6
16+67=83
560 16=6+5+5
16+68=84
561 16=6+6+4
16+71=87
562 16=6+7+3
16+72=88
563 16=6+9+1
16=1+7+8
564 16=7+2+7
16=1+8+7
565 16=7+3+6
16=16=16
566 16=7+4+5
16=2+6+8
567 16=7+5+4
16=2+7+7
568 16=7+6+3
16=2+8+6
569 16=7+7+2
16=3+5+8
570 16=9+1+6
16=3+6+7
571 16=9+2+5
16=3+7+6
572 16=9+3+4
16=3+8+5
573 16=9+4+3
16=4+4+8
574 16=9+5+2
16=4+5+7
575 16=9+6+1
16=4+6+6
576 17+12=29
16=4+7+5
577 17+14=31
16=4+8+4
578 17+15=32
16=5+3+8
579 17+16=33
16=5+4+7
580 17+17=34
16=5+5+6
581 17+1=9+9
16=5+6+5
582 17+19=36
16=5+7+4
583 17+22=39
16=5+8+3
584 17+24=41
16=6+2+8
585 17+25=42
16=6+3+7
586 17+26=43
16=6+4+6
587 17+27=44
16=6+5+5
588 17+29=46
16=6+6+4
589 17+32=49
16=6+7+3
590 17+34=51
16=6+8+2
591 17+35=52
16=7+1+8
592 17+36=53
16=7+2+7
593 17+37=54
16=7+3+6
594 17+39=56
16=7+4+5
595 17+42=59
16=7+5+4
596 17+44=61
16=7+6+3
597 17+45=62
16=7+7+2
598 17+46=63
16=7+8+1
599 17+47=64
16=8+1+7
600 17+49=66
16=8+2+6
601 17+52=69
16=8+3+5
602 17+54=71
16=8+4+4
603 17+55=72
16=8+5+3
604 17+56=73
16=8+6+2
605 17+57=74
16=8+7+1
606 17+59=76
17+11=28
607 17+62=79
17+14=31
608 17+74=91
17+15=32
609 17+75=92
17+16=33
610 17+76=93
17+17=34
611 17+77=94
17+18=35
612 17+79=96
17+21=38
613 17=1+7+9
17+24=41
614 17=1+9+7
17+25=42
615 17=17=17
17+26=43
616 17=2+6+9
17+27=44
617 17=2+9+6
17+28=45
618 17=3+5+9
17+31=48
619 17=3+7+7
17+34=51
620 17=3+9+5
17+35=52
621 17=4+4+9
17+36=53
622 17=4+6+7
17+37=54
623 17=4+7+6
17+38=55
624 17=4+9+4
17+41=58
625 17=5+3+9
17+44=61
626 17=5+5+7
17+45=62
627 17=5+6+6
17+46=63
628 17=5+7+5
17+47=64
629 17=5+9+3
17+48=65
630 17=6+2+9
17+51=68
631 17=6+4+7
17+54=71
632 17=6+5+6
17+55=72
633 17=6+6+5
17+56=73
634 17=6+7+4
17+57=74
635 17=6+9+2
17+58=75
636 17=7+1+9
17+61=78
637 17=7+3+7
17+64=81
638 17=7+4+6
17+65=82
639 17=7+5+5
17+66=83
640 17=7+6+4
17+67=84
641 17=7+7+3
17+68=85
642 17=7+9+1
17+71=88
643 17=9+1+7
17=1+8+8
644 17=9+2+6
17=17=17
645 17=9+3+5
17=2+7+8
646 17=9+4+4
17=2+8+7
647 17=9+5+3
17=3+6+8
648 17=9+6+2
17=3+7+7
649 17=9+7+1
17=3+8+6
650 19+12=31
17=4+5+8
651 19+13=32
17=4+6+7
652 19+14=33
17=4+7+6
653 19+15=34
17=4+8+5
654 19+16=35
17=5+4+8
655 19+17=36
17=5+5+7
656 19+22=41
17=5+6+6
657 19+23=42
17=5+7+5
658 19+24=43
17=5+8+4
659 19+25=44
17=6+3+8
660 19+26=45
17=6+4+7
661 19+27=46
17=6+5+6
662 19+32=51
17=6+6+5
663 19+33=52
17=6+7+4
664 19+34=53
17=6+8+3
665 19+35=54
17=7+2+8
666 19+36=55
17=7+3+7
667 19+37=56
17=7+4+6
668 19+42=61
17=7+5+5
669 19+43=62
17=7+6+4
670 19+44=63
17=7+7+3
671 19+45=64
17=7+8+2
672 19+46=65
17=8+1+8
673 19+47=66
17=8+2+7
674 19+52=71
17=8+3+6
675 19+53=72
17=8+4+5
676 19+54=73
17=8+5+4
677 19+55=74
17=8+6+3
678 19+56=75
17=8+7+2
679 19+57=76
17=8+8+1
680 19+72=91
18+13=31
681 19+73=92
18+14=32
682 19+74=93
18+15=33
683 19+75=94
18+16=34
684 19+76=95
18+17=35
685 19+77=96
18+18=36
686 19=1+9+9
18+23=41
687 19=19=19
18+24=42
688 19=3+7+9
18+25=43
689 19=3+9+7
18+26=44
690 19=4+6+9
18+27=45
691 19=4+9+6
18+28=46
692 19=5+5+9
18+33=51
693 19=5+7+7
18+34=52
694 19=5+9+5
18+35=53
695 19=6+4+9
18+36=54
696 19=6+6+7
18+37=55
697 19=6+7+6
18+38=56
698 19=6+9+4
18+43=61
699 19=7+3+9
18+44=62
700 19=7+5+7
18+45=63
701 19=7+6+6
18+46=64
702 19=7+7+5
18+47=65
703 19=7+9+3
18+48=66
704 19=9+1+9
18+53=71
705 19=9+3+7
18+54=72
706 19=9+4+6
18+55=73
707 19=9+5+5
18+56=74
708 19=9+6+4
18+57=75
709 19=9+7+3
18+58=76
710 19=9+9+1
18+63=81
711 2+1+9=12
18+64=82
712 2+11=4+9
18+65=83
713 2+11=6+7
18+66=84
714 2+11=7+6
18+67=85
715 2+11=9+4
18+68=86
716 2+12=5+9
18=18=18
717 2+12=7+7
18=2+8+8
718 2+12=9+5
18=3+7+8
719 2+13=6+9
18=3+8+7
720 2+13=9+6
18=4+6+8
721 2+14=7+9
18=4+7+7
722 2+14=9+7
18=4+8+6
723 2+16=9+9
18=5+5+8
724 2+2+7=11
18=5+6+7
725 2+2+9=13
18=5+7+6
726 2+3+6=11
18=5+8+5
727 2+3+7=12
18=6+4+8
728 2+3+9=14
18=6+5+7
729 2+4+5=11
18=6+6+6
730 2+4+6=12
18=6+7+5
731 2+4+7=13
18=6+8+4
732 2+4+9=15
18=7+3+8
733 2+5+4=11
18=7+4+7
734 2+5+5=12
18=7+5+6
735 2+5+6=13
18=7+6+5
736 2+5+7=14
18=7+7+4
737 2+5+9=16
18=7+8+3
738 2+6+3=11
18=8+2+8
739 2+6+4=12
18=8+3+7
740 2+6+5=13
18=8+4+6
741 2+6+6=14
18=8+5+5
742 2+6+7=15
18=8+6+4
743 2+6+9=17
18=8+7+3
744 2+7+2=11
18=8+8+2
745 2+7+3=12
2+1+8=11
746 2+7+4=13
2+11=5+8
747 2+7+5=14
2+11=6+7
748 2+7+6=15
2+11=7+6
749 2+7+7=16
2+11=8+5
750 2+9+1=12
2+12=6+8
751 2+9+2=13
2+12=7+7
752 2+9+3=14
2+12=8+6
753 2+9+4=15
2+13=7+8
754 2+9+5=16
2+13=8+7
755 2+9+6=17
2+14=8+8
756 21+11=32
2+2+7=11
757 21+12=33
2+2+8=12
758 21+13=34
2+3+6=11
759 21+14=35
2+3+7=12
760 21+15=36
2+3+8=13
761 21+16=37
2+4+5=11
762 21+21=42
2+4+6=12
763 21+22=43
2+4+7=13
764 21+23=44
2+4+8=14
765 21+24=45
2+5+4=11
766 21+25=46
2+5+5=12
767 21+26=47
2+5+6=13
768 21+31=52
2+5+7=14
769 21+32=53
2+5+8=15
770 21+33=54
2+6+3=11
771 21+34=55
2+6+4=12
772 21+35=56
2+6+5=13
773 21+36=57
2+6+6=14
774 21+41=62
2+6+7=15
775 21+42=63
2+6+8=16
776 21+43=64
2+7+2=11
777 21+44=65
2+7+3=12
778 21+45=66
2+7+4=13
779 21+46=67
2+7+5=14
780 21+51=72
2+7+6=15
781 21+52=73
2+7+7=16
782 21+53=74
2+7+8=17
783 21+54=75
2+8+1=11
784 21+55=76
2+8+2=12
785 21+56=77
2+8+3=13
786 21+71=92
2+8+4=14
787 21+72=93
2+8+5=15
788 21+73=94
2+8+6=16
789 21+74=95
2+8+7=17
790 21+75=96
2+8+8=18
791 21+76=97
21+11=32
792 21=21=21
21+12=33
793 21=3+9+9
21+13=34
794 21=5+7+9
21+14=35
795 21=5+9+7
21+15=36
796 21=6+6+9
21+16=37
797 21=6+9+6
21+17=38
798 21=7+5+9
21+21=42
799 21=7+7+7
21+22=43
800 21=7+9+5
21+23=44
801 21=9+3+9
21+24=45
802 21=9+5+7
21+25=46
803 21=9+6+6
21+26=47
804 21=9+7+5
21+27=48
805 21=9+9+3
21+31=52
806 22+11=33
21+32=53
807 22+12=34
21+33=54
808 22+13=35
21+34=55
809 22+14=36
21+35=56
810 22+15=37
21+36=57
811 22+17=39
21+37=58
812 22+19=41
21+41=62
813 22+21=43
21+42=63
814 22+22=44
21+43=64
815 22+23=45
21+44=65
816 22+24=46
21+45=66
817 22+25=47
21+46=67
818 22+27=49
21+47=68
819 22+29=51
21+51=72
820 22+31=53
21+52=73
821 22+32=54
21+53=74
822 22+33=55
21+54=75
823 22+34=56
21+55=76
824 22+35=57
21+56=77
825 22+37=59
21+57=78
826 22+39=61
21+61=82
827 22+41=63
21+62=83
828 22+42=64
21+63=84
829 22+43=65
21+64=85
830 22+44=66
21+65=86
831 22+45=67
21+66=87
832 22+47=69
21+67=88
833 22+49=71
21=21=21
834 22+51=73
21=5+8+8
835 22+52=74
21=6+7+8
836 22+53=75
21=6+8+7
837 22+54=76
21=7+6+8
838 22+55=77
21=7+7+7
839 22+57=79
21=7+8+6
840 22+69=91
21=8+5+8
841 22+71=93
21=8+6+7
842 22+72=94
21=8+7+6
843 22+73=95
21=8+8+5
844 22+74=96
22+11=33
845 22+75=97
22+12=34
846 22+77=99
22+13=35
847 22=11+11
22+14=36
848 22=22=22
22+15=37
849 22=4+9+9
22+16=38
850 22=6+7+9
22+21=43
851 22=6+9+7
22+22=44
852 22=7+6+9
22+23=45
853 22=7+9+6
22+24=46
854 22=9+4+9
22+25=47
855 22=9+6+7
22+26=48
856 22=9+7+6
22+31=53
857 22=9+9+4
22+32=54
858 23+11=34
22+33=55
859 23+12=35
22+34=56
860 23+13=36
22+35=57
861 23+14=37
22+36=58
862 23+16=39
22+41=63
863 23+19=42
22+42=64
864 23+21=44
22+43=65
865 23+22=45
22+44=66
866 23+23=46
22+45=67
867 23+24=47
22+46=68
868 23+26=49
22+51=73
869 23+29=52
22+52=74
870 23+31=54
22+53=75
871 23+32=55
22+54=76
872 23+33=56
22+55=77
873 23+34=57
22+56=78
874 23+36=59
22+61=83
875 23+39=62
22+62=84
876 23+41=64
22+63=85
877 23+42=65
22+64=86
878 23+43=66
22+65=87
879 23+44=67
22+66=88
880 23+46=69
22=11+11
881 23+49=72
22=22=22
882 23+51=74
22=6+8+8
883 23+52=75
22=7+7+8
884 23+53=76
22=7+8+7
885 23+54=77
22=8+6+8
886 23+56=79
22=8+7+7
887 23+69=92
22=8+8+6
888 23+71=94
23+11=34
889 23+72=95
23+12=35
890 23+73=96
23+13=36
891 23+74=97
23+14=37
892 23+76=99
23+15=38
893 23=11+12
23+18=41
894 23=12+11
23+21=44
895 23=23=23
23+22=45
896 23=5+9+9
23+23=46
897 23=7+7+9
23+24=47
898 23=7+9+7
23+25=48
899 23=9+5+9
23+28=51
900 23=9+7+7
23+31=54
901 23=9+9+5
23+32=55
902 24+11=35
23+33=56
903 24+12=36
23+34=57
904 24+13=37
23+35=58
905 24+15=39
23+38=61
906 24+17=41
23+41=64
907 24+19=43
23+42=65
908 24+21=45
23+43=66
909 24+22=46
23+44=67
910 24+23=47
23+45=68
911 24+25=49
23+48=71
912 24+27=51
23+51=74
913 24+29=53
23+52=75
914 24+31=55
23+53=76
915 24+32=56
23+54=77
916 24+33=57
23+55=78
917 24+35=59
23+58=81
918 24+37=61
23+61=84
919 24+39=63
23+62=85
920 24+41=65
23+63=86
921 24+42=66
23+64=87
922 24+43=67
23+65=88
923 24+45=69
23=11+12
924 24+47=71
23=12+11
925 24+49=73
23=23=23
926 24+51=75
23=7+8+8
927 24+52=76
23=8+7+8
928 24+53=77
23=8+8+7
929 24+55=79
24+11=35
930 24+67=91
24+12=36
931 24+69=93
24+13=37
932 24+71=95
24+14=38
933 24+72=96
24+17=41
934 24+73=97
24+18=42
935 24+75=99
24+21=45
936 24=11+13
24+22=46
937 24=12+12
24+23=47
938 24=13+11
24+24=48
939 24=24=24
24+27=51
940 24=6+9+9
24+28=52
941 24=9+6+9
24+31=55
942 24=9+9+6
24+32=56
943 25+11=36
24+33=57
944 25+12=37
24+34=58
945 25+14=39
24+37=61
946 25+16=41
24+38=62
947 25+17=42
24+41=65
948 25+19=44
24+42=66
949 25+21=46
24+43=67
950 25+22=47
24+44=68
951 25+24=49
24+47=71
952 25+26=51
24+48=72
953 25+27=52
24+51=75
954 25+29=54
24+52=76
955 25+31=56
24+53=77
956 25+32=57
24+54=78
957 25+34=59
24+57=81
958 25+36=61
24+58=82
959 25+37=62
24+61=85
960 25+39=64
24+62=86
961 25+41=66
24+63=87
962 25+42=67
24+64=88
963 25+44=69
24=11+13
964 25+46=71
24=12+12
965 25+47=72
24=13+11
966 25+49=74
24=24=24
967 25+51=76
24=8+8+8
968 25+52=77
25+11=36
969 25+54=79
25+12=37
970 25+66=91
25+13=38
971 25+67=92
25+16=41
972 25+69=94
25+17=42
973 25+71=96
25+18=43
974 25+72=97
25+21=46
975 25+74=99
25+22=47
976 25=11+14
25+23=48
977 25=12+13
25+26=51
978 25=13+12
25+27=52
979 25=14+11
25+28=53
980 25=25=25
25+31=56
981 25=7+9+9
25+32=57
982 25=9+7+9
25+33=58
983 25=9+9+7
25+36=61
984 26+11=37
25+37=62
985 26+13=39
25+38=63
986 26+15=41
25+41=66
987 26+16=42
25+42=67
988 26+17=43
25+43=68
989 26+19=45
25+46=71
990 26+21=47
25+47=72
991 26+23=49
25+48=73
992 26+25=51
25+51=76
993 26+26=52
25+52=77
994 26+27=53
25+53=78
995 26+29=55
25+56=81
996 26+31=57
25+57=82
997 26+33=59
25+58=83
998 26+35=61
25+61=86
999 26+36=62
25+62=87
1000 26+37=63 25+63=88
1001 26+39=65 25=11+14
1002 26+41=67 25=12+13
1003 26+43=69 25=13+12
1004 26+45=71 25=14+11
1005 26+46=72 25=25=25
1006 26+47=73 26+11=37
1007 26+49=75 26+12=38
1008 26+51=77 26+15=41
1009 26+53=79 26+16=42
1010 26+65=91 26+17=43
1011 26+66=92 26+18=44
1012 26+67=93 26+21=47
1013 26+69=95 26+22=48
1014 26+71=97 26+25=51
1015 26+73=99 26+26=52
1016 26=11+15 26+27=53
1017 26=12+14 26+28=54
1018 26=13+13 26+31=57
1019 26=14+12 26+32=58
1020 26=15+11 26+35=61
1021 26=26=26 26+36=62
1022 27+12=39 26+37=63
1023 27+14=41 26+38=64
1024 27+15=42 26+41=67
1025 27+16=43 26+42=68
1026 27+17=44 26+45=71
1027 27+19=46 26+46=72
1028 27+22=49 26+47=73
1029 27+24=51 26+48=74
1030 27+25=52 26+51=77
1031 27+26=53 26+52=78
1032 27+27=54 26+55=81
1033 27+29=56 26+56=82
1034 27+32=59 26+57=83
1035 27+34=61 26+58=84
1036 27+35=62 26+61=87
1037 27+36=63 26+62=88
1038 27+37=64 26=11+15
1039 27+39=66 26=12+14
1040 27+42=69 26=13+13
1041 27+44=71 26=14+12
1042 27+45=72 26=15+11
1043 27+46=73 26=26=26
1044 27+47=74 27+11=38
1045 27+49=76 27+14=41
1046 27+52=79 27+15=42
1047 27+64=91 27+16=43
1048 27+65=92 27+17=44
1049 27+66=93 27+18=45
1050 27+67=94 27+21=48
1051 27+69=96 27+24=51
1052 27+72=99 27+25=52
1053 27=11+16 27+26=53
1054 27=12+15 27+27=54
1055 27=13+14 27+28=55
1056 27=14+13 27+31=58
1057 27=15+12 27+34=61
1058 27=16+11 27+35=62
1059 27=27=27 27+36=63
1060 27=9+9+9 27+37=64
1061 29+12=41 27+38=65
1062 29+13=42 27+41=68
1063 29+14=43 27+44=71
1064 29+15=44 27+45=72
1065 29+16=45 27+46=73
1066 29+17=46 27+47=74
1067 29+22=51 27+48=75
1068 29+23=52 27+51=78
1069 29+24=53 27+54=81
1070 29+25=54 27+55=82
1071 29+26=55 27+56=83
1072 29+27=56 27+57=84
1073 29+32=61 27+58=85
1074 29+33=62 27+61=88
1075 29+34=63 27=11+16
1076 29+35=64 27=12+15
1077 29+36=65 27=13+14
1078 29+37=66 27=14+13
1079 29+42=71 27=15+12
1080 29+43=72 27=16+11
1081 29+44=73 27=27=27
1082 29+45=74 28+13=41
1083 29+46=75 28+14=42
1084 29+47=76 28+15=43
1085 29+62=91 28+16=44
1086 29+63=92 28+17=45
1087 29+64=93 28+18=46
1088 29+65=94 28+23=51
1089 29+66=95 28+24=52
1090 29+67=96 28+25=53
1091 29=12+17 28+26=54
1092 29=13+16 28+27=55
1093 29=14+15 28+28=56
1094 29=15+14 28+33=61
1095 29=16+13 28+34=62
1096 29=17+12 28+35=63
1097 29=29=29 28+36=64
1098 3+1+7=11 28+37=65
1099 3+1+9=13 28+38=66
1100 3+11=5+9 28+43=71
1101 3+11=7+7 28+44=72
1102 3+11=9+5 28+45=73
1103 3+12=6+9 28+46=74
1104 3+12=9+6 28+47=75
1105 3+13=7+9 28+48=76
1106 3+13=9+7 28+53=81
1107 3+15=9+9 28+54=82
1108 3+2+6=11 28+55=83
1109 3+2+7=12 28+56=84
1110 3+2+9=14 28+57=85
1111 3+3+5=11 28+58=86
1112 3+3+6=12 28=11+17
1113 3+3+7=13 28=12+16
1114 3+3+9=15 28=13+15
1115 3+4+4=11 28=14+14
1116 3+4+5=12 28=15+13
1117 3+4+6=13 28=16+12
1118 3+4+7=14 28=17+11
1119 3+4+9=16 28=28=28
1120 3+5+3=11 3+1+7=11
1121 3+5+4=12 3+1+8=12
1122 3+5+5=13 3+11=6+8
1123 3+5+6=14 3+11=7+7
1124 3+5+7=15 3+11=8+6
1125 3+5+9=17 3+12=7+8
1126 3+6+2=11 3+12=8+7
1127 3+6+3=12 3+13=8+8
1128 3+6+4=13 3+2+6=11
1129 3+6+5=14 3+2+7=12
1130 3+6+6=15 3+2+8=13
1131 3+6+7=16 3+3+5=11
1132 3+7+1=11 3+3+6=12
1133 3+7+2=12 3+3+7=13
1134 3+7+3=13 3+3+8=14
1135 3+7+4=14 3+4+4=11
1136 3+7+5=15 3+4+5=12
1137 3+7+6=16 3+4+6=13
1138 3+7+7=17 3+4+7=14
1139 3+7+9=19 3+4+8=15
1140 3+9+1=13 3+5+3=11
1141 3+9+2=14 3+5+4=12
1142 3+9+3=15 3+5+5=13
1143 3+9+4=16 3+5+6=14
1144 3+9+5=17 3+5+7=15
1145 3+9+7=19 3+5+8=16
1146 3+9+9=21 3+6+2=11
1147 3+9=1+11 3+6+3=12
1148 3+9=11+1 3+6+4=13
1149 31+11=42 3+6+5=14
1150 31+12=43 3+6+6=15
1151 31+13=44 3+6+7=16
1152 31+14=45 3+6+8=17
1153 31+15=46 3+7+1=11
1154 31+16=47 3+7+2=12
1155 31+21=52 3+7+3=13
1156 31+22=53 3+7+4=14
1157 31+23=54 3+7+5=15
1158 31+24=55 3+7+6=16
1159 31+25=56 3+7+7=17
1160 31+26=57 3+7+8=18
1161 31+31=62 3+8+1=12
1162 31+32=63 3+8+2=13
1163 31+33=64 3+8+3=14
1164 31+34=65 3+8+4=15
1165 31+35=66 3+8+5=16
1166 31+36=67 3+8+6=17
1167 31+41=72 3+8+7=18
1168 31+42=73 31+11=42
1169 31+43=74 31+12=43
1170 31+44=75 31+13=44
1171 31+45=76 31+14=45
1172 31+46=77 31+15=46
1173 31+61=92 31+16=47
1174 31+62=93 31+17=48
1175 31+63=94 31+21=52
1176 31+64=95 31+22=53
1177 31+65=96 31+23=54
1178 31+66=97 31+24=55
1179 31=12+19 31+25=56
1180 31=14+17 31+26=57
1181 31=15+16 31+27=58
1182 31=16+15 31+31=62
1183 31=17+14 31+32=63
1184 31=19+12 31+33=64
1185 31=31=31 31+34=65
1186 32+11=43 31+35=66
1187 32+12=44 31+36=67
1188 32+13=45 31+37=68
1189 32+14=46 31+41=72
1190 32+15=47 31+42=73
1191 32+17=49 31+43=74
1192 32+19=51 31+44=75
1193 32+21=53 31+45=76
1194 32+22=54 31+46=77
1195 32+23=55 31+47=78
1196 32+24=56 31+51=82
1197 32+25=57 31+52=83
1198 32+27=59 31+53=84
1199 32+29=61 31+54=85
1200 32+31=63 31+55=86
1201 32+32=64 31+56=87
1202 32+33=65 31+57=88
1203 32+34=66 31=13+18
1204 32+35=67 31=14+17
1205 32+37=69 31=15+16
1206 32+39=71 31=16+15
1207 32+41=73 31=17+14
1208 32+42=74 31=18+13
1209 32+43=75 31=31=31
1210 32+44=76 32+11=43
1211 32+45=77 32+12=44
1212 32+47=79 32+13=45
1213 32+59=91 32+14=46
1214 32+61=93 32+15=47
1215 32+62=94 32+16=48
1216 32+63=95 32+21=53
1217 32+64=96 32+22=54
1218 32+65=97 32+23=55
1219 32+67=99 32+24=56
1220 32=11+21 32+25=57
1221 32=13+19 32+26=58
1222 32=15+17 32+31=63
1223 32=16+16 32+32=64
1224 32=17+15 32+33=65
1225 32=19+13 32+34=66
1226 32=21+11 32+35=67
1227 32=32=32 32+36=68
1228 33+11=44 32+41=73
1229 33+12=45 32+42=74
1230 33+13=46 32+43=75
1231 33+14=47 32+44=76
1232 33+16=49 32+45=77
1233 33+19=52 32+46=78
1234 33+21=54 32+51=83
1235 33+22=55 32+52=84
1236 33+23=56 32+53=85
1237 33+24=57 32+54=86
1238 33+26=59 32+55=87
1239 33+29=62 32+56=88
1240 33+31=64 32=11+21
1241 33+32=65 32=14+18
1242 33+33=66 32=15+17
1243 33+34=67 32=16+16
1244 33+36=69 32=17+15
1245 33+39=72 32=18+14
1246 33+41=74 32=21+11
1247 33+42=75 32=32=32
1248 33+43=76 33+11=44
1249 33+44=77 33+12=45
1250 33+46=79 33+13=46
1251 33+59=92 33+14=47
1252 33+61=94 33+15=48
1253 33+62=95 33+18=51
1254 33+63=96 33+21=54
1255 33+64=97 33+22=55
1256 33+66=99 33+23=56
1257 33=11+22 33+24=57
1258 33=12+21 33+25=58
1259 33=14+19 33+28=61
1260 33=16+17 33+31=64
1261 33=17+16 33+32=65
1262 33=19+14 33+33=66
1263 33=21+12 33+34=67
1264 33=22+11 33+35=68
1265 33=33=33 33+38=71
1266 34+11=45 33+41=74
1267 34+12=46 33+42=75
1268 34+13=47 33+43=76
1269 34+15=49 33+44=77
1270 34+17=51 33+45=78
1271 34+19=53 33+48=81
1272 34+21=55 33+51=84
1273 34+22=56 33+52=85
1274 34+23=57 33+53=86
1275 34+25=59 33+54=87
1276 34+27=61 33+55=88
1277 34+29=63 33=11+22
1278 34+31=65 33=12+21
1279 34+32=66 33=15+18
1280 34+33=67 33=16+17
1281 34+35=69 33=17+16
1282 34+37=71 33=18+15
1283 34+39=73 33=21+12
1284 34+41=75 33=22+11
1285 34+42=76 33=33=33
1286 34+43=77 34+11=45
1287 34+45=79 34+12=46
1288 34+57=91 34+13=47
1289 34+59=93 34+14=48
1290 34+61=95 34+17=51
1291 34+62=96 34+18=52
1292 34+63=97 34+21=55
1293 34+65=99 34+22=56
1294 34=11+23 34+23=57
1295 34=12+22 34+24=58
1296 34=13+21 34+27=61
1297 34=15+19 34+28=62
1298 34=17+17 34+31=65
1299 34=19+15 34+32=66
1300 34=21+13 34+33=67
1301 34=22+12 34+34=68
1302 34=23+11 34+37=71
1303 34=34=34 34+38=72
1304 35+11=46 34+41=75
1305 35+12=47 34+42=76
1306 35+14=49 34+43=77
1307 35+16=51 34+44=78
1308 35+17=52 34+47=81
1309 35+19=54 34+48=82
1310 35+21=56 34+51=85
1311 35+22=57 34+52=86
1312 35+24=59 34+53=87
1313 35+26=61 34+54=88
1314 35+27=62 34=11+23
1315 35+29=64 34=12+22
1316 35+31=66 34=13+21
1317 35+32=67 34=16+18
1318 35+34=69 34=17+17
1319 35+36=71 34=18+16
1320 35+37=72 34=21+13
1321 35+39=74 34=22+12
1322 35+41=76 34=23+11
1323 35+42=77 34=34=34
1324 35+44=79 35+11=46
1325 35+56=91 35+12=47
1326 35+57=92 35+13=48
1327 35+59=94 35+16=51
1328 35+61=96 35+17=52
1329 35+62=97 35+18=53
1330 35+64=99 35+21=56
1331 35=11+24 35+22=57
1332 35=12+23 35+23=58
1333 35=13+22 35+26=61
1334 35=14+21 35+27=62
1335 35=16+19 35+28=63
1336 35=19+16 35+31=66
1337 35=21+14 35+32=67
1338 35=22+13 35+33=68
1339 35=23+12 35+36=71
1340 35=24+11 35+37=72
1341 35=35=35 35+38=73
1342 36+11=47 35+41=76
1343 36+13=49 35+42=77
1344 36+15=51 35+43=78
1345 36+16=52 35+46=81
1346 36+17=53 35+47=82
1347 36+19=55 35+48=83
1348 36+21=57 35+51=86
1349 36+23=59 35+52=87
1350 36+25=61 35+53=88
1351 36+26=62 35=11+24
1352 36+27=63 35=12+23
1353 36+29=65 35=13+22
1354 36+31=67 35=14+21
1355 36+33=69 35=17+18
1356 36+35=71 35=18+17
1357 36+36=72 35=21+14
1358 36+37=73 35=22+13
1359 36+39=75 35=23+12
1360 36+41=77 35=24+11
1361 36+43=79 35=35=35
1362 36+55=91 36+11=47
1363 36+56=92 36+12=48
1364 36+57=93 36+15=51
1365 36+59=95 36+16=52
1366 36+61=97 36+17=53
1367 36+63=99 36+18=54
1368 36=11+25 36+21=57
1369 36=12+24 36+22=58
1370 36=13+23 36+25=61
1371 36=14+22 36+26=62
1372 36=15+21 36+27=63
1373 36=17+19 36+28=64
1374 36=19+17 36+31=67
1375 36=21+15 36+32=68
1376 36=22+14 36+35=71
1377 36=23+13 36+36=72
1378 36=24+12 36+37=73
1379 36=25+11 36+38=74
1380 36=36=36 36+41=77
1381 37+12=49 36+42=78
1382 37+14=51 36+45=81
1383 37+15=52 36+46=82
1384 37+16=53 36+47=83
1385 37+17=54 36+48=84
1386 37+19=56 36+51=87
1387 37+22=59 36+52=88
1388 37+24=61 36=11+25
1389 37+25=62 36=12+24
1390 37+26=63 36=13+23
1391 37+27=64 36=14+22
1392 37+29=66 36=15+21
1393 37+32=69 36=18+18
1394 37+34=71 36=21+15
1395 37+35=72 36=22+14
1396 37+36=73 36=23+13
1397 37+37=74 36=24+12
1398 37+39=76 36=25+11
1399 37+42=79 36=36=36
1400 37+54=91 37+11=48
1401 37+55=92 37+14=51
1402 37+56=93 37+15=52
1403 37+57=94 37+16=53
1404 37+59=96 37+17=54
1405 37+62=99 37+18=55
1406 37=11+26 37+21=58
1407 37=12+25 37+24=61
1408 37=13+24 37+25=62
1409 37=14+23 37+26=63
1410 37=15+22 37+27=64
1411 37=16+21 37+28=65
1412 37=21+16 37+31=68
1413 37=22+15 37+34=71
1414 37=23+14 37+35=72
1415 37=24+13 37+36=73
1416 37=25+12 37+37=74
1417 37=26+11 37+38=75
1418 37=37=37 37+41=78
1419 39+12=51 37+44=81
1420 39+13=52 37+45=82
1421 39+14=53 37+46=83
1422 39+15=54 37+47=84
1423 39+16=55 37+48=85
1424 39+17=56 37+51=88
1425 39+22=61 37=11+26
1426 39+23=62 37=12+25
1427 39+24=63 37=13+24
1428 39+25=64 37=14+23
1429 39+26=65 37=15+22
1430 39+27=66 37=16+21
1431 39+32=71 37=21+16
1432 39+33=72 37=22+15
1433 39+34=73 37=23+14
1434 39+35=74 37=24+13
1435 39+36=75 37=25+12
1436 39+37=76 37=26+11
1437 39+52=91 37=37=37
1438 39+53=92 38+13=51
1439 39+54=93 38+14=52
1440 39+55=94 38+15=53
1441 39+56=95 38+16=54
1442 39+57=96 38+17=55
1443 39=12+27 38+18=56
1444 39=13+26 38+23=61
1445 39=14+25 38+24=62
1446 39=15+24 38+25=63
1447 39=16+23 38+26=64
1448 39=17+22 38+27=65
1449 39=22+17 38+28=66
1450 39=23+16 38+33=71
1451 39=24+15 38+34=72
1452 39=25+14 38+35=73
1453 39=26+13 38+36=74
1454 39=27+12 38+37=75
1455 39=39=39 38+38=76
1456 4+1+6=11 38+43=81
1457 4+1+7=12 38+44=82
1458 4+1+9=14 38+45=83
1459 4+11=6+9 38+46=84
1460 4+11=9+6 38+47=85
1461 4+12=7+9 38+48=86
1462 4+12=9+7 38=11+27
1463 4+14=9+9 38=12+26
1464 4+2+5=11 38=13+25
1465 4+2+6=12 38=14+24
1466 4+2+7=13 38=15+23
1467 4+2+9=15 38=16+22
1468 4+3+4=11 38=17+21
1469 4+3+5=12 38=21+17
1470 4+3+6=13 38=22+16
1471 4+3+7=14 38=23+15
1472 4+3+9=16 38=24+14
1473 4+4+3=11 38=25+13
1474 4+4+4=12 38=26+12
1475 4+4+5=13 38=27+11
1476 4+4+6=14 38=38=38
1477 4+4+7=15 4+1+6=11
1478 4+4+9=17 4+1+7=12
1479 4+5+2=11 4+1+8=13
1480 4+5+3=12 4+11=7+8
1481 4+5+4=13 4+11=8+7
1482 4+5+5=14 4+12=8+8
1483 4+5+6=15 4+2+5=11
1484 4+5+7=16 4+2+6=12
1485 4+6+1=11 4+2+7=13
1486 4+6+2=12 4+2+8=14
1487 4+6+3=13 4+3+4=11
1488 4+6+4=14 4+3+5=12
1489 4+6+5=15 4+3+6=13
1490 4+6+6=16 4+3+7=14
1491 4+6+7=17 4+3+8=15
1492 4+6+9=19 4+4+3=11
1493 4+7+1=12 4+4+4=12
1494 4+7+2=13 4+4+5=13
1495 4+7+3=14 4+4+6=14
1496 4+7+4=15 4+4+7=15
1497 4+7+5=16 4+4+8=16
1498 4+7+6=17 4+5+2=11
1499 4+9+1=14 4+5+3=12
1500 4+9+2=15 4+5+4=13
1501 4+9+3=16 4+5+5=14
1502 4+9+4=17 4+5+6=15
1503 4+9+6=19 4+5+7=16
1504 4+9+9=22 4+5+8=17
1505 4+9=1+12 4+6+1=11
1506 4+9=11+2 4+6+2=12
1507 4+9=12+1 4+6+3=13
1508 4+9=2+11 4+6+4=14
1509 41+11=52 4+6+5=15
1510 41+12=53 4+6+6=16
1511 41+13=54 4+6+7=17
1512 41+14=55 4+6+8=18
1513 41+15=56 4+7+1=12
1514 41+16=57 4+7+2=13
1515 41+21=62 4+7+3=14
1516 41+22=63 4+7+4=15
1517 41+23=64 4+7+5=16
1518 41+24=65 4+7+6=17
1519 41+25=66 4+7+7=18
1520 41+26=67 4+8+1=13
1521 41+31=72 4+8+2=14
1522 41+32=73 4+8+3=15
1523 41+33=74 4+8+4=16
1524 41+34=75 4+8+5=17
1525 41+35=76 4+8+6=18
1526 41+36=77 4+8=1+11
1527 41+51=92 4+8=11+1
1528 41+52=93 41+11=52
1529 41+53=94 41+12=53
1530 41+54=95 41+13=54
1531 41+55=96 41+14=55
1532 41+56=97 41+15=56
1533 41=12+29 41+16=57
1534 41=14+27 41+17=58
1535 41=15+26 41+21=62
1536 41=16+25 41+22=63
1537 41=17+24 41+23=64
1538 41=19+22 41+24=65
1539 41=22+19 41+25=66
1540 41=24+17 41+26=67
1541 41=25+16 41+27=68
1542 41=26+15 41+31=72
1543 41=27+14 41+32=73
1544 41=29+12 41+33=74
1545 41=41=41 41+34=75
1546 42+11=53 41+35=76
1547 42+12=54 41+36=77
1548 42+13=55 41+37=78
1549 42+14=56 41+41=82
1550 42+15=57 41+42=83
1551 42+17=59 41+43=84
1552 42+19=61 41+44=85
1553 42+21=63 41+45=86
1554 42+22=64 41+46=87
1555 42+23=65 41+47=88
1556 42+24=66 41=13+28
1557 42+25=67 41=14+27
1558 42+27=69 41=15+26
1559 42+29=71 41=16+25
1560 42+31=73 41=17+24
1561 42+32=74 41=18+23
1562 42+33=75 41=23+18
1563 42+34=76 41=24+17
1564 42+35=77 41=25+16
1565 42+37=79 41=26+15
1566 42+49=91 41=27+14
1567 42+51=93 41=28+13
1568 42+52=94 41=41=41
1569 42+53=95 42+11=53
1570 42+54=96 42+12=54
1571 42+55=97 42+13=55
1572 42+57=99 42+14=56
1573 42=11+31 42+15=57
1574 42=13+29 42+16=58
1575 42=15+27 42+21=63
1576 42=16+26 42+22=64
1577 42=17+25 42+23=65
1578 42=19+23 42+24=66
1579 42=21+21 42+25=67
1580 42=23+19 42+26=68
1581 42=25+17 42+31=73
1582 42=26+16 42+32=74
1583 42=27+15 42+33=75
1584 42=29+13 42+34=76
1585 42=31+11 42+35=77
1586 42=42=42 42+36=78
1587 43+11=54 42+41=83
1588 43+12=55 42+42=84
1589 43+13=56 42+43=85
1590 43+14=57 42+44=86
1591 43+16=59 42+45=87
1592 43+19=62 42+46=88
1593 43+21=64 42=11+31
1594 43+22=65 42=14+28
1595 43+23=66 42=15+27
1596 43+24=67 42=16+26
1597 43+26=69 42=17+25
1598 43+29=72 42=18+24
1599 43+31=74 42=21+21
1600 43+32=75 42=24+18
1601 43+33=76 42=25+17
1602 43+34=77 42=26+16
1603 43+36=79 42=27+15
1604 43+49=92 42=28+14
1605 43+51=94 42=31+11
1606 43+52=95 42=42=42
1607 43+53=96 43+11=54
1608 43+54=97 43+12=55
1609 43+56=99 43+13=56
1610 43=11+32 43+14=57
1611 43=12+31 43+15=58
1612 43=14+29 43+18=61
1613 43=16+27 43+21=64
1614 43=17+26 43+22=65
1615 43=19+24 43+23=66
1616 43=21+22 43+24=67
1617 43=22+21 43+25=68
1618 43=24+19 43+28=71
1619 43=26+17 43+31=74
1620 43=27+16 43+32=75
1621 43=29+14 43+33=76
1622 43=31+12 43+34=77
1623 43=32+11 43+35=78
1624 43=43=43 43+38=81
1625 44+11=55 43+41=84
1626 44+12=56 43+42=85
1627 44+13=57 43+43=86
1628 44+15=59 43+44=87
1629 44+17=61 43+45=88
1630 44+19=63 43=11+32
1631 44+21=65 43=12+31
1632 44+22=66 43=15+28
1633 44+23=67 43=16+27
1634 44+25=69 43=17+26
1635 44+27=71 43=18+25
1636 44+29=73 43=21+22
1637 44+31=75 43=22+21
1638 44+32=76 43=25+18
1639 44+33=77 43=26+17
1640 44+35=79 43=27+16
1641 44+47=91 43=28+15
1642 44+49=93 43=31+12
1643 44+51=95 43=32+11
1644 44+52=96 43=43=43
1645 44+53=97 44+11=55
1646 44+55=99 44+12=56
1647 44=11+33 44+13=57
1648 44=12+32 44+14=58
1649 44=13+31 44+17=61
1650 44=15+29 44+18=62
1651 44=17+27 44+21=65
1652 44=19+25 44+22=66
1653 44=21+23 44+23=67
1654 44=22+22 44+24=68
1655 44=23+21 44+27=71
1656 44=25+19 44+28=72
1657 44=27+17 44+31=75
1658 44=29+15 44+32=76
1659 44=31+13 44+33=77
1660 44=32+12 44+34=78
1661 44=33+11 44+37=81
1662 44=44=44 44+38=82
1663 45+11=56 44+41=85
1664 45+12=57 44+42=86
1665 45+14=59 44+43=87
1666 45+16=61 44+44=88
1667 45+17=62 44=11+33
1668 45+19=64 44=12+32
1669 45+21=66 44=13+31
1670 45+22=67 44=16+28
1671 45+24=69 44=17+27
1672 45+26=71 44=18+26
1673 45+27=72 44=21+23
1674 45+29=74 44=22+22
1675 45+31=76 44=23+21
1676 45+32=77 44=26+18
1677 45+34=79 44=27+17
1678 45+46=91 44=28+16
1679 45+47=92 44=31+13
1680 45+49=94 44=32+12
1681 45+51=96 44=33+11
1682 45+52=97 44=44=44
1683 45+54=99 45+11=56
1684 45=11+34 45+12=57
1685 45=12+33 45+13=58
1686 45=13+32 45+16=61
1687 45=14+31 45+17=62
1688 45=16+29 45+18=63
1689 45=19+26 45+21=66
1690 45=21+24 45+22=67
1691 45=22+23 45+23=68
1692 45=23+22 45+26=71
1693 45=24+21 45+27=72
1694 45=26+19 45+28=73
1695 45=29+16 45+31=76
1696 45=31+14 45+32=77
1697 45=32+13 45+33=78
1698 45=33+12 45+36=81
1699 45=34+11 45+37=82
1700 45=45=45 45+38=83
1701 46+11=57 45+41=86
1702 46+13=59 45+42=87
1703 46+15=61 45+43=88
1704 46+16=62 45=11+34
1705 46+17=63 45=12+33
1706 46+19=65 45=13+32
1707 46+21=67 45=14+31
1708 46+23=69 45=17+28
1709 46+25=71 45=18+27
1710 46+26=72 45=21+24
1711 46+27=73 45=22+23
1712 46+29=75 45=23+22
1713 46+31=77 45=24+21
1714 46+33=79 45=27+18
1715 46+45=91 45=28+17
1716 46+46=92 45=31+14
1717 46+47=93 45=32+13
1718 46+49=95 45=33+12
1719 46+51=97 45=34+11
1720 46+53=99 45=45=45
1721 46=11+35 46+11=57
1722 46=12+34 46+12=58
1723 46=13+33 46+15=61
1724 46=14+32 46+16=62
1725 46=15+31 46+17=63
1726 46=17+29 46+18=64
1727 46=19+27 46+21=67
1728 46=21+25 46+22=68
1729 46=22+24 46+25=71
1730 46=23+23 46+26=72
1731 46=24+22 46+27=73
1732 46=25+21 46+28=74
1733 46=27+19 46+31=77
1734 46=29+17 46+32=78
1735 46=31+15 46+35=81
1736 46=32+14 46+36=82
1737 46=33+13 46+37=83
1738 46=34+12 46+38=84
1739 46=35+11 46+41=87
1740 46=46=46 46+42=88
1741 47+12=59 46=11+35
1742 47+14=61 46=12+34
1743 47+15=62 46=13+33
1744 47+16=63 46=14+32
1745 47+17=64 46=15+31
1746 47+19=66 46=18+28
1747 47+22=69 46=21+25
1748 47+24=71 46=22+24
1749 47+25=72 46=23+23
1750 47+26=73 46=24+22
1751 47+27=74 46=25+21
1752 47+29=76 46=28+18
1753 47+32=79 46=31+15
1754 47+44=91 46=32+14
1755 47+45=92 46=33+13
1756 47+46=93 46=34+12
1757 47+47=94 46=35+11
1758 47+49=96 46=46=46
1759 47+52=99 47+11=58
1760 47=11+36 47+14=61
1761 47=12+35 47+15=62
1762 47=13+34 47+16=63
1763 47=14+33 47+17=64
1764 47=15+32 47+18=65
1765 47=16+31 47+21=68
1766 47=21+26 47+24=71
1767 47=22+25 47+25=72
1768 47=23+24 47+26=73
1769 47=24+23 47+27=74
1770 47=25+22 47+28=75
1771 47=26+21 47+31=78
1772 47=31+16 47+34=81
1773 47=32+15 47+35=82
1774 47=33+14 47+36=83
1775 47=34+13 47+37=84
1776 47=35+12 47+38=85
1777 47=36+11 47+41=88
1778 47=47=47 47=11+36
1779 49+12=61 47=12+35
1780 49+13=62 47=13+34
1781 49+14=63 47=14+33
1782 49+15=64 47=15+32
1783 49+16=65 47=16+31
1784 49+17=66 47=21+26
1785 49+22=71 47=22+25
1786 49+23=72 47=23+24
1787 49+24=73 47=24+23
1788 49+25=74 47=25+22
1789 49+26=75 47=26+21
1790 49+27=76 47=31+16
1791 49+42=91 47=32+15
1792 49+43=92 47=33+14
1793 49+44=93 47=34+13
1794 49+45=94 47=35+12
1795 49+46=95 47=36+11
1796 49+47=96 47=47=47
1797 49=12+37 48+13=61
1798 49=13+36 48+14=62
1799 49=14+35 48+15=63
1800 49=15+34 48+16=64
1801 49=16+33 48+17=65
1802 49=17+32 48+18=66
1803 49=22+27 48+23=71
1804 49=23+26 48+24=72
1805 49=24+25 48+25=73
1806 49=25+24 48+26=74
1807 49=26+23 48+27=75
1808 49=27+22 48+28=76
1809 49=32+17 48+33=81
1810 49=33+16 48+34=82
1811 49=34+15 48+35=83
1812 49=35+14 48+36=84
1813 49=36+13 48+37=85
1814 49=37+12 48+38=86
1815 49=49=49 48=11+37
1816 5+1+5=11 48=12+36
1817 5+1+6=12 48=13+35
1818 5+1+7=13 48=14+34
1819 5+1+9=15 48=15+33
1820 5+11=7+9 48=16+32
1821 5+11=9+7 48=17+31
1822 5+13=9+9 48=21+27
1823 5+2+4=11 48=22+26
1824 5+2+5=12 48=23+25
1825 5+2+6=13 48=24+24
1826 5+2+7=14 48=25+23
1827 5+2+9=16 48=26+22
1828 5+3+3=11 48=27+21
1829 5+3+4=12 48=31+17
1830 5+3+5=13 48=32+16
1831 5+3+6=14 48=33+15
1832 5+3+7=15 48=34+14
1833 5+3+9=17 48=35+13
1834 5+4+2=11 48=36+12
1835 5+4+3=12 48=37+11
1836 5+4+4=13 48=48=48
1837 5+4+5=14 5+1+5=11
1838 5+4+6=15 5+1+6=12
1839 5+4+7=16 5+1+7=13
1840 5+5+1=11 5+1+8=14
1841 5+5+2=12 5+11=8+8
1842 5+5+3=13 5+2+4=11
1843 5+5+4=14 5+2+5=12
1844 5+5+5=15 5+2+6=13
1845 5+5+6=16 5+2+7=14
1846 5+5+7=17 5+2+8=15
1847 5+5+9=19 5+3+3=11
1848 5+6+1=12 5+3+4=12
1849 5+6+2=13 5+3+5=13
1850 5+6+3=14 5+3+6=14
1851 5+6+4=15 5+3+7=15
1852 5+6+5=16 5+3+8=16
1853 5+6+6=17 5+4+2=11
1854 5+7+1=13 5+4+3=12
1855 5+7+2=14 5+4+4=13
1856 5+7+3=15 5+4+5=14
1857 5+7+4=16 5+4+6=15
1858 5+7+5=17 5+4+7=16
1859 5+7+7=19 5+4+8=17
1860 5+7+9=21 5+5+1=11
1861 5+7=1+11 5+5+2=12
1862 5+7=11+1 5+5+3=13
1863 5+9+1=15 5+5+4=14
1864 5+9+2=16 5+5+5=15
1865 5+9+3=17 5+5+6=16
1866 5+9+5=19 5+5+7=17
1867 5+9+7=21 5+5+8=18
1868 5+9+9=23 5+6+1=12
1869 5+9=1+13 5+6+2=13
1870 5+9=11+3 5+6+3=14
1871 5+9=12+2 5+6+4=15
1872 5+9=13+1 5+6+5=16
1873 5+9=2+12 5+6+6=17
1874 5+9=3+11 5+6+7=18
1875 51+11=62 5+7+1=13
1876 51+12=63 5+7+2=14
1877 51+13=64 5+7+3=15
1878 51+14=65 5+7+4=16
1879 51+15=66 5+7+5=17
1880 51+16=67 5+7+6=18
1881 51+21=72 5+7=1+11
1882 51+22=73 5+7=11+1
1883 51+23=74 5+8+1=14
1884 51+24=75 5+8+2=15
1885 51+25=76 5+8+3=16
1886 51+26=77 5+8+4=17
1887 51+41=92 5+8+5=18
1888 51+42=93 5+8+8=21
1889 51+43=94 5+8=1+12
1890 51+44=95 5+8=11+2
1891 51+45=96 5+8=12+1
1892 51+46=97 5+8=2+11
1893 51=12+39 51+11=62
1894 51=14+37 51+12=63
1895 51=15+36 51+13=64
1896 51=16+35 51+14=65
1897 51=17+34 51+15=66
1898 51=19+32 51+16=67
1899 51=22+29 51+17=68
1900 51=24+27 51+21=72
1901 51=25+26 51+22=73
1902 51=26+25 51+23=74
1903 51=27+24 51+24=75
1904 51=29+22 51+25=76
1905 51=32+19 51+26=77
1906 51=34+17 51+27=78
1907 51=35+16 51+31=82
1908 51=36+15 51+32=83
1909 51=37+14 51+33=84
1910 51=39+12 51+34=85
1911 51=51=51 51+35=86
1912 52+11=63 51+36=87
1913 52+12=64 51+37=88
1914 52+13=65 51=13+38
1915 52+14=66 51=14+37
1916 52+15=67 51=15+36
1917 52+17=69 51=16+35
1918 52+19=71 51=17+34
1919 52+21=73 51=18+33
1920 52+22=74 51=23+28
1921 52+23=75 51=24+27
1922 52+24=76 51=25+26
1923 52+25=77 51=26+25
1924 52+27=79 51=27+24
1925 52+39=91 51=28+23
1926 52+41=93 51=33+18
1927 52+42=94 51=34+17
1928 52+43=95 51=35+16
1929 52+44=96 51=36+15
1930 52+45=97 51=37+14
1931 52+47=99 51=38+13
1932 52=11+41 51=51=51
1933 52=13+39 52+11=63
1934 52=15+37 52+12=64
1935 52=16+36 52+13=65
1936 52=17+35 52+14=66
1937 52=19+33 52+15=67
1938 52=21+31 52+16=68
1939 52=23+29 52+21=73
1940 52=25+27 52+22=74
1941 52=26+26 52+23=75
1942 52=27+25 52+24=76
1943 52=29+23 52+25=77
1944 52=31+21 52+26=78
1945 52=33+19 52+31=83
1946 52=35+17 52+32=84
1947 52=36+16 52+33=85
1948 52=37+15 52+34=86
1949 52=39+13 52+35=87
1950 52=41+11 52+36=88
1951 52=52=52 52=11+41
1952 53+11=64 52=14+38
1953 53+12=65 52=15+37
1954 53+13=66 52=16+36
1955 53+14=67 52=17+35
1956 53+16=69 52=18+34
1957 53+19=72 52=21+31
1958 53+21=74 52=24+28
1959 53+22=75 52=25+27
1960 53+23=76 52=26+26
1961 53+24=77 52=27+25
1962 53+26=79 52=28+24
1963 53+39=92 52=31+21
1964 53+41=94 52=34+18
1965 53+42=95 52=35+17
1966 53+43=96 52=36+16
1967 53+44=97 52=37+15
1968 53+46=99 52=38+14
1969 53=11+42 52=41+11
1970 53=12+41 52=52=52
1971 53=14+39 53+11=64
1972 53=16+37 53+12=65
1973 53=17+36 53+13=66
1974 53=19+34 53+14=67
1975 53=21+32 53+15=68
1976 53=22+31 53+18=71
1977 53=24+29 53+21=74
1978 53=26+27 53+22=75
1979 53=27+26 53+23=76
1980 53=29+24 53+24=77
1981 53=31+22 53+25=78
1982 53=32+21 53+28=81
1983 53=34+19 53+31=84
1984 53=36+17 53+32=85
1985 53=37+16 53+33=86
1986 53=39+14 53+34=87
1987 53=41+12 53+35=88
1988 53=42+11 53=11+42
1989 53=53=53 53=12+41
1990 54+11=65 53=15+38
1991 54+12=66 53=16+37
1992 54+13=67 53=17+36
1993 54+15=69 53=18+35
1994 54+17=71 53=21+32
1995 54+19=73 53=22+31
1996 54+21=75 53=25+28
1997 54+22=76 53=26+27
1998 54+23=77 53=27+26
1999 54+25=79 53=28+25
2000 54+37=91 53=31+22
2001 54+39=93 53=32+21
2002 54+41=95 53=35+18
2003 54+42=96 53=36+17
2004 54+43=97 53=37+16
2005 54+45=99 53=38+15
2006 54=11+43 53=41+12
2007 54=12+42 53=42+11
2008 54=13+41 53=53=53
2009 54=15+39 54+11=65
2010 54=17+37 54+12=66
2011 54=19+35 54+13=67
2012 54=21+33 54+14=68
2013 54=22+32 54+17=71
2014 54=23+31 54+18=72
2015 54=25+29 54+21=75
2016 54=27+27 54+22=76
2017 54=29+25 54+23=77
2018 54=31+23 54+24=78
2019 54=32+22 54+27=81
2020 54=33+21 54+28=82
2021 54=35+19 54+31=85
2022 54=37+17 54+32=86
2023 54=39+15 54+33=87
2024 54=41+13 54+34=88
2025 54=42+12 54=11+43
2026 54=43+11 54=12+42
2027 54=54=54 54=13+41
2028 55+11=66 54=16+38
2029 55+12=67 54=17+37
2030 55+14=69 54=18+36
2031 55+16=71 54=21+33
2032 55+17=72 54=22+32
2033 55+19=74 54=23+31
2034 55+21=76 54=26+28
2035 55+22=77 54=27+27
2036 55+24=79 54=28+26
2037 55+36=91 54=31+23
2038 55+37=92 54=32+22
2039 55+39=94 54=33+21
2040 55+41=96 54=36+18
2041 55+42=97 54=37+17
2042 55+44=99 54=38+16
2043 55=11+44 54=41+13
2044 55=12+43 54=42+12
2045 55=13+42 54=43+11
2046 55=14+41 54=54=54
2047 55=16+39 55+11=66
2048 55=19+36 55+12=67
2049 55=21+34 55+13=68
2050 55=22+33 55+16=71
2051 55=23+32 55+17=72
2052 55=24+31 55+18=73
2053 55=26+29 55+21=76
2054 55=29+26 55+22=77
2055 55=31+24 55+23=78
2056 55=32+23 55+26=81
2057 55=33+22 55+27=82
2058 55=34+21 55+28=83
2059 55=36+19 55+31=86
2060 55=39+16 55+32=87
2061 55=41+14 55+33=88
2062 55=42+13 55=11+44
2063 55=43+12 55=12+43
2064 55=44+11 55=13+42
2065 55=55=55 55=14+41
2066 56+11=67 55=17+38
2067 56+13=69 55=18+37
2068 56+15=71 55=21+34
2069 56+16=72 55=22+33
2070 56+17=73 55=23+32
2071 56+19=75 55=24+31
2072 56+21=77 55=27+28
2073 56+23=79 55=28+27
2074 56+35=91 55=31+24
2075 56+36=92 55=32+23
2076 56+37=93 55=33+22
2077 56+39=95 55=34+21
2078 56+41=97 55=37+18
2079 56+43=99 55=38+17
2080 56=11+45 55=41+14
2081 56=12+44 55=42+13
2082 56=13+43 55=43+12
2083 56=14+42 55=44+11
2084 56=15+41 55=55=55
2085 56=17+39 56+11=67
2086 56=19+37 56+12=68
2087 56=21+35 56+15=71
2088 56=22+34 56+16=72
2089 56=23+33 56+17=73
2090 56=24+32 56+18=74
2091 56=25+31 56+21=77
2092 56=27+29 56+22=78
2093 56=29+27 56+25=81
2094 56=31+25 56+26=82
2095 56=32+24 56+27=83
2096 56=33+23 56+28=84
2097 56=34+22 56+31=87
2098 56=35+21 56+32=88
2099 56=37+19 56=11+45
2100 56=39+17 56=12+44
2101 56=41+15 56=13+43
2102 56=42+14 56=14+42
2103 56=43+13 56=15+41
2104 56=44+12 56=18+38
2105 56=45+11 56=21+35
2106 56=56=56 56=22+34
2107 57+12=69 56=23+33
2108 57+14=71 56=24+32
2109 57+15=72 56=25+31
2110 57+16=73 56=28+28
2111 57+17=74 56=31+25
2112 57+19=76 56=32+24
2113 57+22=79 56=33+23
2114 57+34=91 56=34+22
2115 57+35=92 56=35+21
2116 57+36=93 56=38+18
2117 57+37=94 56=41+15
2118 57+39=96 56=42+14
2119 57+42=99 56=43+13
2120 57=11+46 56=44+12
2121 57=12+45 56=45+11
2122 57=13+44 56=56=56
2123 57=14+43 57+11=68
2124 57=15+42 57+14=71
2125 57=16+41 57+15=72
2126 57=21+36 57+16=73
2127 57=22+35 57+17=74
2128 57=23+34 57+18=75
2129 57=24+33 57+21=78
2130 57=25+32 57+24=81
2131 57=26+31 57+25=82
2132 57=31+26 57+26=83
2133 57=32+25 57+27=84
2134 57=33+24 57+28=85
2135 57=34+23 57+31=88
2136 57=35+22 57=11+46
2137 57=36+21 57=12+45
2138 57=41+16 57=13+44
2139 57=42+15 57=14+43
2140 57=43+14 57=15+42
2141 57=44+13 57=16+41
2142 57=45+12 57=21+36
2143 57=46+11 57=22+35
2144 57=57=57 57=23+34
2145 59+12=71 57=24+33
2146 59+13=72 57=25+32
2147 59+14=73 57=26+31
2148 59+15=74 57=31+26
2149 59+16=75 57=32+25
2150 59+17=76 57=33+24
2151 59+32=91 57=34+23
2152 59+33=92 57=35+22
2153 59+34=93 57=36+21
2154 59+35=94 57=41+16
2155 59+36=95 57=42+15
2156 59+37=96 57=43+14
2157 59=12+47 57=44+13
2158 59=13+46 57=45+12
2159 59=14+45 57=46+11
2160 59=15+44 57=57=57
2161 59=16+43 58+13=71
2162 59=17+42 58+14=72
2163 59=22+37 58+15=73
2164 59=23+36 58+16=74
2165 59=24+35 58+17=75
2166 59=25+34 58+18=76
2167 59=26+33 58+23=81
2168 59=27+32 58+24=82
2169 59=32+27 58+25=83
2170 59=33+26 58+26=84
2171 59=34+25 58+27=85
2172 59=35+24 58+28=86
2173 59=36+23 58=11+47
2174 59=37+22 58=12+46
2175 59=42+17 58=13+45
2176 59=43+16 58=14+44
2177 59=44+15 58=15+43
2178 59=45+14 58=16+42
2179 59=46+13 58=17+41
2180 59=47+12 58=21+37
2181 59=59=59 58=22+36
2182 6+1+4=11 58=23+35
2183 6+1+5=12 58=24+34
2184 6+1+6=13 58=25+33
2185 6+1+7=14 58=26+32
2186 6+1+9=16 58=27+31
2187 6+12=9+9 58=31+27
2188 6+2+3=11 58=32+26
2189 6+2+4=12 58=33+25
2190 6+2+5=13 58=34+24
2191 6+2+6=14 58=35+23
2192 6+2+7=15 58=36+22
2193 6+2+9=17 58=37+21
2194 6+3+2=11 58=41+17
2195 6+3+3=12 58=42+16
2196 6+3+4=13 58=43+15
2197 6+3+5=14 58=44+14
2198 6+3+6=15 58=45+13
2199 6+3+7=16 58=46+12
2200 6+4+1=11 58=47+11
2201 6+4+2=12 58=58=58
2202 6+4+3=13 6+1+4=11
2203 6+4+4=14 6+1+5=12
2204 6+4+5=15 6+1+6=13
2205 6+4+6=16 6+1+7=14
2206 6+4+7=17 6+1+8=15
2207 6+4+9=19 6+2+3=11
2208 6+5+1=12 6+2+4=12
2209 6+5+2=13 6+2+5=13
2210 6+5+3=14 6+2+6=14
2211 6+5+4=15 6+2+7=15
2212 6+5+5=16 6+2+8=16
2213 6+5+6=17 6+3+2=11
2214 6+6+1=13 6+3+3=12
2215 6+6+2=14 6+3+4=13
2216 6+6+3=15 6+3+5=14
2217 6+6+4=16 6+3+6=15
2218 6+6+5=17 6+3+7=16
2219 6+6+7=19 6+3+8=17
2220 6+6+9=21 6+4+1=11
2221 6+6=1+11 6+4+2=12
2222 6+6=11+1 6+4+3=13
2223 6+7+1=14 6+4+4=14
2224 6+7+2=15 6+4+5=15
2225 6+7+3=16 6+4+6=16
2226 6+7+4=17 6+4+7=17
2227 6+7+6=19 6+4+8=18
2228 6+7+9=22 6+5+1=12
2229 6+7=1+12 6+5+2=13
2230 6+7=11+2 6+5+3=14
2231 6+7=12+1 6+5+4=15
2232 6+7=2+11 6+5+5=16
2233 6+9+1=16 6+5+6=17
2234 6+9+2=17 6+5+7=18
2235 6+9+4=19 6+6+1=13
2236 6+9+6=21 6+6+2=14
2237 6+9+7=22 6+6+3=15
2238 6+9+9=24 6+6+4=16
2239 6+9=1+14 6+6+5=17
2240 6+9=11+4 6+6+6=18
2241 6+9=12+3 6+6=1+11
2242 6+9=13+2 6+6=11+1
2243 6+9=14+1 6+7+1=14
2244 6+9=2+13 6+7+2=15
2245 6+9=3+12 6+7+3=16
2246 6+9=4+11 6+7+4=17
2247 61+11=72 6+7+5=18
2248 61+12=73 6+7+8=21
2249 61+13=74 6+7=1+12
2250 61+14=75 6+7=11+2
2251 61+15=76 6+7=12+1
2252 61+16=77 6+7=2+11
2253 61+31=92 6+8+1=15
2254 61+32=93 6+8+2=16
2255 61+33=94 6+8+3=17
2256 61+34=95 6+8+4=18
2257 61+35=96 6+8+7=21
2258 61+36=97 6+8+8=22
2259 61=12+49 6+8=1+13
2260 61=14+47 6+8=11+3
2261 61=15+46 6+8=12+2
2262 61=16+45 6+8=13+1
2263 61=17+44 6+8=2+12
2264 61=19+42 6+8=3+11
2265 61=22+39 61+11=72
2266 61=24+37 61+12=73
2267 61=25+36 61+13=74
2268 61=26+35 61+14=75
2269 61=27+34 61+15=76
2270 61=29+32 61+16=77
2271 61=32+29 61+17=78
2272 61=34+27 61+21=82
2273 61=35+26 61+22=83
2274 61=36+25 61+23=84
2275 61=37+24 61+24=85
2276 61=39+22 61+25=86
2277 61=42+19 61+26=87
2278 61=44+17 61+27=88
2279 61=45+16 61=13+48
2280 61=46+15 61=14+47
2281 61=47+14 61=15+46
2282 61=49+12 61=16+45
2283 61=61=61 61=17+44
2284 62+11=73 61=18+43
2285 62+12=74 61=23+38
2286 62+13=75 61=24+37
2287 62+14=76 61=25+36
2288 62+15=77 61=26+35
2289 62+17=79 61=27+34
2290 62+29=91 61=28+33
2291 62+31=93 61=33+28
2292 62+32=94 61=34+27
2293 62+33=95 61=35+26
2294 62+34=96 61=36+25
2295 62+35=97 61=37+24
2296 62+37=99 61=38+23
2297 62=11+51 61=43+18
2298 62=13+49 61=44+17
2299 62=15+47 61=45+16
2300 62=16+46 61=46+15
2301 62=17+45 61=47+14
2302 62=19+43 61=48+13
2303 62=21+41 61=61=61
2304 62=23+39 62+11=73
2305 62=25+37 62+12=74
2306 62=26+36 62+13=75
2307 62=27+35 62+14=76
2308 62=29+33 62+15=77
2309 62=31+31 62+16=78
2310 62=33+29 62+21=83
2311 62=35+27 62+22=84
2312 62=36+26 62+23=85
2313 62=37+25 62+24=86
2314 62=39+23 62+25=87
2315 62=41+21 62+26=88
2316 62=43+19 62=11+51
2317 62=45+17 62=14+48
2318 62=46+16 62=15+47
2319 62=47+15 62=16+46
2320 62=49+13 62=17+45
2321 62=51+11 62=18+44
2322 62=62=62 62=21+41
2323 63+11=74 62=24+38
2324 63+12=75 62=25+37
2325 63+13=76 62=26+36
2326 63+14=77 62=27+35
2327 63+16=79 62=28+34
2328 63+29=92 62=31+31
2329 63+31=94 62=34+28
2330 63+32=95 62=35+27
2331 63+33=96 62=36+26
2332 63+34=97 62=37+25
2333 63+36=99 62=38+24
2334 63=11+52 62=41+21
2335 63=12+51 62=44+18
2336 63=14+49 62=45+17
2337 63=16+47 62=46+16
2338 63=17+46 62=47+15
2339 63=19+44 62=48+14
2340 63=21+42 62=51+11
2341 63=22+41 62=62=62
2342 63=24+39 63+11=74
2343 63=26+37 63+12=75
2344 63=27+36 63+13=76
2345 63=29+34 63+14=77
2346 63=31+32 63+15=78
2347 63=32+31 63+18=81
2348 63=34+29 63+21=84
2349 63=36+27 63+22=85
2350 63=37+26 63+23=86
2351 63=39+24 63+24=87
2352 63=41+22 63+25=88
2353 63=42+21 63=11+52
2354 63=44+19 63=12+51
2355 63=46+17 63=15+48
2356 63=47+16 63=16+47
2357 63=49+14 63=17+46
2358 63=51+12 63=18+45
2359 63=52+11 63=21+42
2360 63=63=63 63=22+41
2361 64+11=75 63=25+38
2362 64+12=76 63=26+37
2363 64+13=77 63=27+36
2364 64+15=79 63=28+35
2365 64+27=91 63=31+32
2366 64+29=93 63=32+31
2367 64+31=95 63=35+28
2368 64+32=96 63=36+27
2369 64+33=97 63=37+26
2370 64+35=99 63=38+25
2371 64=11+53 63=41+22
2372 64=12+52 63=42+21
2373 64=13+51 63=45+18
2374 64=15+49 63=46+17
2375 64=17+47 63=47+16
2376 64=19+45 63=48+15
2377 64=21+43 63=51+12
2378 64=22+42 63=52+11
2379 64=23+41 63=63=63
2380 64=25+39 64+11=75
2381 64=27+37 64+12=76
2382 64=29+35 64+13=77
2383 64=31+33 64+14=78
2384 64=32+32 64+17=81
2385 64=33+31 64+18=82
2386 64=35+29 64+21=85
2387 64=37+27 64+22=86
2388 64=39+25 64+23=87
2389 64=41+23 64+24=88
2390 64=42+22 64=11+53
2391 64=43+21 64=12+52
2392 64=45+19 64=13+51
2393 64=47+17 64=16+48
2394 64=49+15 64=17+47
2395 64=51+13 64=18+46
2396 64=52+12 64=21+43
2397 64=53+11 64=22+42
2398 64=64=64 64=23+41
2399 65+11=76 64=26+38
2400 65+12=77 64=27+37
2401 65+14=79 64=28+36
2402 65+26=91 64=31+33
2403 65+27=92 64=32+32
2404 65+29=94 64=33+31
2405 65+31=96 64=36+28
2406 65+32=97 64=37+27
2407 65+34=99 64=38+26
2408 65=11+54 64=41+23
2409 65=12+53 64=42+22
2410 65=13+52 64=43+21
2411 65=14+51 64=46+18
2412 65=16+49 64=47+17
2413 65=19+46 64=48+16
2414 65=21+44 64=51+13
2415 65=22+43 64=52+12
2416 65=23+42 64=53+11
2417 65=24+41 64=64=64
2418 65=26+39 65+11=76
2419 65=29+36 65+12=77
2420 65=31+34 65+13=78
2421 65=32+33 65+16=81
2422 65=33+32 65+17=82
2423 65=34+31 65+18=83
2424 65=36+29 65+21=86
2425 65=39+26 65+22=87
2426 65=41+24 65+23=88
2427 65=42+23 65=11+54
2428 65=43+22 65=12+53
2429 65=44+21 65=13+52
2430 65=46+19 65=14+51
2431 65=49+16 65=17+48
2432 65=51+14 65=18+47
2433 65=52+13 65=21+44
2434 65=53+12 65=22+43
2435 65=54+11 65=23+42
2436 65=65=65 65=24+41
2437 66+11=77 65=27+38
2438 66+13=79 65=28+37
2439 66+25=91 65=31+34
2440 66+26=92 65=32+33
2441 66+27=93 65=33+32
2442 66+29=95 65=34+31
2443 66+31=97 65=37+28
2444 66+33=99 65=38+27
2445 66=11+55 65=41+24
2446 66=12+54 65=42+23
2447 66=13+53 65=43+22
2448 66=14+52 65=44+21
2449 66=15+51 65=47+18
2450 66=17+49 65=48+17
2451 66=19+47 65=51+14
2452 66=21+45 65=52+13
2453 66=22+44 65=53+12
2454 66=23+43 65=54+11
2455 66=24+42 65=65=65
2456 66=25+41 66+11=77
2457 66=27+39 66+12=78
2458 66=29+37 66+15=81
2459 66=31+35 66+16=82
2460 66=32+34 66+17=83
2461 66=33+33 66+18=84
2462 66=34+32 66+21=87
2463 66=35+31 66+22=88
2464 66=37+29 66=11+55
2465 66=39+27 66=12+54
2466 66=41+25 66=13+53
2467 66=42+24 66=14+52
2468 66=43+23 66=15+51
2469 66=44+22 66=18+48
2470 66=45+21 66=21+45
2471 66=47+19 66=22+44
2472 66=49+17 66=23+43
2473 66=51+15 66=24+42
2474 66=52+14 66=25+41
2475 66=53+13 66=28+38
2476 66=54+12 66=31+35
2477 66=55+11 66=32+34
2478 66=66=66 66=33+33
2479 67+12=79 66=34+32
2480 67+24=91 66=35+31
2481 67+25=92 66=38+28
2482 67+26=93 66=41+25
2483 67+27=94 66=42+24
2484 67+29=96 66=43+23
2485 67+32=99 66=44+22
2486 67=11+56 66=45+21
2487 67=12+55 66=48+18
2488 67=13+54 66=51+15
2489 67=14+53 66=52+14
2490 67=15+52 66=53+13
2491 67=16+51 66=54+12
2492 67=21+46 66=55+11
2493 67=22+45 66=66=66
2494 67=23+44 67+11=78
2495 67=24+43 67+14=81
2496 67=25+42 67+15=82
2497 67=26+41 67+16=83
2498 67=31+36 67+17=84
2499 67=32+35 67+18=85
2500 67=33+34 67+21=88
2501 67=34+33 67=11+56
2502 67=35+32 67=12+55
2503 67=36+31 67=13+54
2504 67=41+26 67=14+53
2505 67=42+25 67=15+52
2506 67=43+24 67=16+51
2507 67=44+23 67=21+46
2508 67=45+22 67=22+45
2509 67=46+21 67=23+44
2510 67=51+16 67=24+43
2511 67=52+15 67=25+42
2512 67=53+14 67=26+41
2513 67=54+13 67=31+36
2514 67=55+12 67=32+35
2515 67=56+11 67=33+34
2516 67=67=67 67=34+33
2517 69+22=91 67=35+32
2518 69+23=92 67=36+31
2519 69+24=93 67=41+26
2520 69+25=94 67=42+25
2521 69+26=95 67=43+24
2522 69+27=96 67=44+23
2523 69=12+57 67=45+22
2524 69=13+56 67=46+21
2525 69=14+55 67=51+16
2526 69=15+54 67=52+15
2527 69=16+53 67=53+14
2528 69=17+52 67=54+13
2529 69=22+47 67=55+12
2530 69=23+46 67=56+11
2531 69=24+45 67=67=67
2532 69=25+44 68+13=81
2533 69=26+43 68+14=82
2534 69=27+42 68+15=83
2535 69=32+37 68+16=84
2536 69=33+36 68+17=85
2537 69=34+35 68+18=86
2538 69=35+34 68=11+57
2539 69=36+33 68=12+56
2540 69=37+32 68=13+55
2541 69=42+27 68=14+54
2542 69=43+26 68=15+53
2543 69=44+25 68=16+52
2544 69=45+24 68=17+51
2545 69=46+23 68=21+47
2546 69=47+22 68=22+46
2547 69=52+17 68=23+45
2548 69=53+16 68=24+44
2549 69=54+15 68=25+43
2550 69=55+14 68=26+42
2551 69=56+13 68=27+41
2552 69=57+12 68=31+37
2553 69=69=69 68=32+36
2554 7+1+3=11 68=33+35
2555 7+1+4=12 68=34+34
2556 7+1+5=13 68=35+33
2557 7+1+6=14 68=36+32
2558 7+1+7=15 68=37+31
2559 7+1+9=17 68=41+27
2560 7+11=9+9 68=42+26
2561 7+2+2=11 68=43+25
2562 7+2+3=12 68=44+24
2563 7+2+4=13 68=45+23
2564 7+2+5=14 68=46+22
2565 7+2+6=15 68=47+21
2566 7+2+7=16 68=51+17
2567 7+3+1=11 68=52+16
2568 7+3+2=12 68=53+15
2569 7+3+3=13 68=54+14
2570 7+3+4=14 68=55+13
2571 7+3+5=15 68=56+12
2572 7+3+6=16 68=57+11
2573 7+3+7=17 68=68=68
2574 7+3+9=19 7+1+3=11
2575 7+4+1=12 7+1+4=12
2576 7+4+2=13 7+1+5=13
2577 7+4+3=14 7+1+6=14
2578 7+4+4=15 7+1+7=15
2579 7+4+5=16 7+1+8=16
2580 7+4+6=17 7+2+2=11
2581 7+5+1=13 7+2+3=12
2582 7+5+2=14 7+2+4=13
2583 7+5+3=15 7+2+5=14
2584 7+5+4=16 7+2+6=15
2585 7+5+5=17 7+2+7=16
2586 7+5+7=19 7+2+8=17
2587 7+5+9=21 7+3+1=11
2588 7+5=1+11 7+3+2=12
2589 7+5=11+1 7+3+3=13
2590 7+6+1=14 7+3+4=14
2591 7+6+2=15 7+3+5=15
2592 7+6+3=16 7+3+6=16
2593 7+6+4=17 7+3+7=17
2594 7+6+6=19 7+3+8=18
2595 7+6+9=22 7+4+1=12
2596 7+6=1+12 7+4+2=13
2597 7+6=11+2 7+4+3=14
2598 7+6=12+1 7+4+4=15
2599 7+6=2+11 7+4+5=16
2600 7+7+1=15 7+4+6=17
2601 7+7+2=16 7+4+7=18
2602 7+7+3=17 7+5+1=13
2603 7+7+5=19 7+5+2=14
2604 7+7+7=21 7+5+3=15
2605 7+7+9=23 7+5+4=16
2606 7+7=1+13 7+5+5=17
2607 7+7=11+3 7+5+6=18
2608 7+7=12+2 7+5=1+11
2609 7+7=13+1 7+5=11+1
2610 7+7=2+12 7+6+1=14
2611 7+7=3+11 7+6+2=15
2612 7+9+1=17 7+6+3=16
2613 7+9+3=19 7+6+4=17
2614 7+9+5=21 7+6+5=18
2615 7+9+6=22 7+6+8=21
2616 7+9+7=23 7+6=1+12
2617 7+9+9=25 7+6=11+2
2618 7+9=1+15 7+6=12+1
2619 7+9=11+5 7+6=2+11
2620 7+9=12+4 7+7+1=15
2621 7+9=13+3 7+7+2=16
2622 7+9=14+2 7+7+3=17
2623 7+9=15+1 7+7+4=18
2624 7+9=2+14 7+7+7=21
2625 7+9=3+13 7+7+8=22
2626 7+9=4+12 7+7=1+13
2627 7+9=5+11 7+7=11+3
2628 71+21=92 7+7=12+2
2629 71+22=93 7+7=13+1
2630 71+23=94 7+7=2+12
2631 71+24=95 7+7=3+11
2632 71+25=96 7+8+1=16
2633 71+26=97 7+8+2=17
2634 71=12+59 7+8+3=18
2635 71=14+57 7+8+6=21
2636 71=15+56 7+8+7=22
2637 71=16+55 7+8+8=23
2638 71=17+54 7+8=1+14
2639 71=19+52 7+8=11+4
2640 71=22+49 7+8=12+3
2641 71=24+47 7+8=13+2
2642 71=25+46 7+8=14+1
2643 71=26+45 7+8=2+13
2644 71=27+44 7+8=3+12
2645 71=29+42 7+8=4+11
2646 71=32+39 71+11=82
2647 71=34+37 71+12=83
2648 71=35+36 71+13=84
2649 71=36+35 71+14=85
2650 71=37+34 71+15=86
2651 71=39+32 71+16=87
2652 71=42+29 71+17=88
2653 71=44+27 71=13+58
2654 71=45+26 71=14+57
2655 71=46+25 71=15+56
2656 71=47+24 71=16+55
2657 71=49+22 71=17+54
2658 71=52+19 71=18+53
2659 71=54+17 71=23+48
2660 71=55+16 71=24+47
2661 71=56+15 71=25+46
2662 71=57+14 71=26+45
2663 71=59+12 71=27+44
2664 71=71=71 71=28+43
2665 72+19=91 71=33+38
2666 72+21=93 71=34+37
2667 72+22=94 71=35+36
2668 72+23=95 71=36+35
2669 72+24=96 71=37+34
2670 72+25=97 71=38+33
2671 72+27=99 71=43+28
2672 72=11+61 71=44+27
2673 72=13+59 71=45+26
2674 72=15+57 71=46+25
2675 72=16+56 71=47+24
2676 72=17+55 71=48+23
2677 72=19+53 71=53+18
2678 72=21+51 71=54+17
2679 72=23+49 71=55+16
2680 72=25+47 71=56+15
2681 72=26+46 71=57+14
2682 72=27+45 71=58+13
2683 72=29+43 71=71=71
2684 72=31+41 72+11=83
2685 72=33+39 72+12=84
2686 72=35+37 72+13=85
2687 72=36+36 72+14=86
2688 72=37+35 72+15=87
2689 72=39+33 72+16=88
2690 72=41+31 72=11+61
2691 72=43+29 72=14+58
2692 72=45+27 72=15+57
2693 72=46+26 72=16+56
2694 72=47+25 72=17+55
2695 72=49+23 72=18+54
2696 72=51+21 72=21+51
2697 72=53+19 72=24+48
2698 72=55+17 72=25+47
2699 72=56+16 72=26+46
2700 72=57+15 72=27+45
2701 72=59+13 72=28+44
2702 72=61+11 72=31+41
2703 72=72=72 72=34+38
2704 73+19=92 72=35+37
2705 73+21=94 72=36+36
2706 73+22=95 72=37+35
2707 73+23=96 72=38+34
2708 73+24=97 72=41+31
2709 73+26=99 72=44+28
2710 73=11+62 72=45+27
2711 73=12+61 72=46+26
2712 73=14+59 72=47+25
2713 73=16+57 72=48+24
2714 73=17+56 72=51+21
2715 73=19+54 72=54+18
2716 73=21+52 72=55+17
2717 73=22+51 72=56+16
2718 73=24+49 72=57+15
2719 73=26+47 72=58+14
2720 73=27+46 72=61+11
2721 73=29+44 72=72=72
2722 73=31+42 73+11=84
2723 73=32+41 73+12=85
2724 73=34+39 73+13=86
2725 73=36+37 73+14=87
2726 73=37+36 73+15=88
2727 73=39+34 73=11+62
2728 73=41+32 73=12+61
2729 73=42+31 73=15+58
2730 73=44+29 73=16+57
2731 73=46+27 73=17+56
2732 73=47+26 73=18+55
2733 73=49+24 73=21+52
2734 73=51+22 73=22+51
2735 73=52+21 73=25+48
2736 73=54+19 73=26+47
2737 73=56+17 73=27+46
2738 73=57+16 73=28+45
2739 73=59+14 73=31+42
2740 73=61+12 73=32+41
2741 73=62+11 73=35+38
2742 73=73=73 73=36+37
2743 74+17=91 73=37+36
2744 74+19=93 73=38+35
2745 74+21=95 73=41+32
2746 74+22=96 73=42+31
2747 74+23=97 73=45+28
2748 74+25=99 73=46+27
2749 74=11+63 73=47+26
2750 74=12+62 73=48+25
2751 74=13+61 73=51+22
2752 74=15+59 73=52+21
2753 74=17+57 73=55+18
2754 74=19+55 73=56+17
2755 74=21+53 73=57+16
2756 74=22+52 73=58+15
2757 74=23+51 73=61+12
2758 74=25+49 73=62+11
2759 74=27+47 73=73=73
2760 74=29+45 74+11=85
2761 74=31+43 74+12=86
2762 74=32+42 74+13=87
2763 74=33+41 74+14=88
2764 74=35+39 74=11+63
2765 74=37+37 74=12+62
2766 74=39+35 74=13+61
2767 74=41+33 74=16+58
2768 74=42+32 74=17+57
2769 74=43+31 74=18+56
2770 74=45+29 74=21+53
2771 74=47+27 74=22+52
2772 74=49+25 74=23+51
2773 74=51+23 74=26+48
2774 74=52+22 74=27+47
2775 74=53+21 74=28+46
2776 74=55+19 74=31+43
2777 74=57+17 74=32+42
2778 74=59+15 74=33+41
2779 74=61+13 74=36+38
2780 74=62+12 74=37+37
2781 74=63+11 74=38+36
2782 74=74=74 74=41+33
2783 75+16=91 74=42+32
2784 75+17=92 74=43+31
2785 75+19=94 74=46+28
2786 75+21=96 74=47+27
2787 75+22=97 74=48+26
2788 75+24=99 74=51+23
2789 75=11+64 74=52+22
2790 75=12+63 74=53+21
2791 75=13+62 74=56+18
2792 75=14+61 74=57+17
2793 75=16+59 74=58+16
2794 75=19+56 74=61+13
2795 75=21+54 74=62+12
2796 75=22+53 74=63+11
2797 75=23+52 74=74=74
2798 75=24+51 75+11=86
2799 75=26+49 75+12=87
2800 75=29+46 75+13=88
2801 75=31+44 75=11+64
2802 75=32+43 75=12+63
2803 75=33+42 75=13+62
2804 75=34+41 75=14+61
2805 75=36+39 75=17+58
2806 75=39+36 75=18+57
2807 75=41+34 75=21+54
2808 75=42+33 75=22+53
2809 75=43+32 75=23+52
2810 75=44+31 75=24+51
2811 75=46+29 75=27+48
2812 75=49+26 75=28+47
2813 75=51+24 75=31+44
2814 75=52+23 75=32+43
2815 75=53+22 75=33+42
2816 75=54+21 75=34+41
2817 75=56+19 75=37+38
2818 75=59+16 75=38+37
2819 75=61+14 75=41+34
2820 75=62+13 75=42+33
2821 75=63+12 75=43+32
2822 75=64+11 75=44+31
2823 75=75=75 75=47+28
2824 76+15=91 75=48+27
2825 76+16=92 75=51+24
2826 76+17=93 75=52+23
2827 76+19=95 75=53+22
2828 76+21=97 75=54+21
2829 76+23=99 75=57+18
2830 76=11+65 75=58+17
2831 76=12+64 75=61+14
2832 76=13+63 75=62+13
2833 76=14+62 75=63+12
2834 76=15+61 75=64+11
2835 76=17+59 75=75=75
2836 76=19+57 76+11=87
2837 76=21+55 76+12=88
2838 76=22+54 76=11+65
2839 76=23+53 76=12+64
2840 76=24+52 76=13+63
2841 76=25+51 76=14+62
2842 76=27+49 76=15+61
2843 76=29+47 76=18+58
2844 76=31+45 76=21+55
2845 76=32+44 76=22+54
2846 76=33+43 76=23+53
2847 76=34+42 76=24+52
2848 76=35+41 76=25+51
2849 76=37+39 76=28+48
2850 76=39+37 76=31+45
2851 76=41+35 76=32+44
2852 76=42+34 76=33+43
2853 76=43+33 76=34+42
2854 76=44+32 76=35+41
2855 76=45+31 76=38+38
2856 76=47+29 76=41+35
2857 76=49+27 76=42+34
2858 76=51+25 76=43+33
2859 76=52+24 76=44+32
2860 76=53+23 76=45+31
2861 76=54+22 76=48+28
2862 76=55+21 76=51+25
2863 76=57+19 76=52+24
2864 76=59+17 76=53+23
2865 76=61+15 76=54+22
2866 76=62+14 76=55+21
2867 76=63+13 76=58+18
2868 76=64+12 76=61+15
2869 76=65+11 76=62+14
2870 76=76=76 76=63+13
2871 77+14=91 76=64+12
2872 77+15=92 76=65+11
2873 77+16=93 76=76=76
2874 77+17=94 77+11=88
2875 77+19=96 77=11+66
2876 77+22=99 77=12+65
2877 77=11+66 77=13+64
2878 77=12+65 77=14+63
2879 77=13+64 77=15+62
2880 77=14+63 77=16+61
2881 77=15+62 77=21+56
2882 77=16+61 77=22+55
2883 77=21+56 77=23+54
2884 77=22+55 77=24+53
2885 77=23+54 77=25+52
2886 77=24+53 77=26+51
2887 77=25+52 77=31+46
2888 77=26+51 77=32+45
2889 77=31+46 77=33+44
2890 77=32+45 77=34+43
2891 77=33+44 77=35+42
2892 77=34+43 77=36+41
2893 77=35+42 77=41+36
2894 77=36+41 77=42+35
2895 77=41+36 77=43+34
2896 77=42+35 77=44+33
2897 77=43+34 77=45+32
2898 77=44+33 77=46+31
2899 77=45+32 77=51+26
2900 77=46+31 77=52+25
2901 77=51+26 77=53+24
2902 77=52+25 77=54+23
2903 77=53+24 77=55+22
2904 77=54+23 77=56+21
2905 77=55+22 77=61+16
2906 77=56+21 77=62+15
2907 77=61+16 77=63+14
2908 77=62+15 77=64+13
2909 77=63+14 77=65+12
2910 77=64+13 77=66+11
2911 77=65+12 77=77=77
2912 77=66+11 78=11+67
2913 77=77=77 78=12+66
2914 79+12=91 78=13+65
2915 79+13=92 78=14+64
2916 79+14=93 78=15+63
2917 79+15=94 78=16+62
2918 79+16=95 78=17+61
2919 79+17=96 78=21+57
2920 79=12+67 78=22+56
2921 79=13+66 78=23+55
2922 79=14+65 78=24+54
2923 79=15+64 78=25+53
2924 79=16+63 78=26+52
2925 79=17+62 78=27+51
2926 79=22+57 78=31+47
2927 79=23+56 78=32+46
2928 79=24+55 78=33+45
2929 79=25+54 78=34+44
2930 79=26+53 78=35+43
2931 79=27+52 78=36+42
2932 79=32+47 78=37+41
2933 79=33+46 78=41+37
2934 79=34+45 78=42+36
2935 79=35+44 78=43+35
2936 79=36+43 78=44+34
2937 79=37+42 78=45+33
2938 79=42+37 78=46+32
2939 79=43+36 78=47+31
2940 79=44+35 78=51+27
2941 79=45+34 78=52+26
2942 79=46+33 78=53+25
2943 79=47+32 78=54+24
2944 79=52+27 78=55+23
2945 79=53+26 78=56+22
2946 79=54+25 78=57+21
2947 79=55+24 78=61+17
2948 79=56+23 78=62+16
2949 79=57+22 78=63+15
2950 79=62+17 78=64+14
2951 79=63+16 78=65+13
2952 79=64+15 78=66+12
2953 79=65+14 78=67+11
2954 79=66+13 78=78=78
2955 79=67+12 8+1+2=11
2956 79=79=79 8+1+3=12
2957 9+1+1=11 8+1+4=13
2958 9+1+2=12 8+1+5=14
2959 9+1+3=13 8+1+6=15
2960 9+1+4=14 8+1+7=16
2961 9+1+5=15 8+1+8=17
2962 9+1+6=16 8+2+1=11
2963 9+1+7=17 8+2+2=12
2964 9+1+9=19 8+2+3=13
2965 9+2+1=12 8+2+4=14
2966 9+2+2=13 8+2+5=15
2967 9+2+3=14 8+2+6=16
2968 9+2+4=15 8+2+7=17
2969 9+2+5=16 8+2+8=18
2970 9+2+6=17 8+3+1=12
2971 9+3+1=13 8+3+2=13
2972 9+3+2=14 8+3+3=14
2973 9+3+3=15 8+3+4=15
2974 9+3+4=16 8+3+5=16
2975 9+3+5=17 8+3+6=17
2976 9+3+7=19 8+3+7=18
2977 9+3+9=21 8+4+1=13
2978 9+3=1+11 8+4+2=14
2979 9+3=11+1 8+4+3=15
2980 9+4+1=14 8+4+4=16
2981 9+4+2=15 8+4+5=17
2982 9+4+3=16 8+4+6=18
2983 9+4+4=17 8+4=1+11
2984 9+4+6=19 8+4=11+1
2985 9+4+9=22 8+5+1=14
2986 9+4=1+12 8+5+2=15
2987 9+4=11+2 8+5+3=16
2988 9+4=12+1 8+5+4=17
2989 9+4=2+11 8+5+5=18
2990 9+5+1=15 8+5+8=21
2991 9+5+2=16 8+5=1+12
2992 9+5+3=17 8+5=11+2
2993 9+5+5=19 8+5=12+1
2994 9+5+7=21 8+5=2+11
2995 9+5+9=23 8+6+1=15
2996 9+5=1+13 8+6+2=16
2997 9+5=11+3 8+6+3=17
2998 9+5=12+2 8+6+4=18
2999 9+5=13+1 8+6+7=21
3000 9+5=2+12 8+6+8=22
3001 9+5=3+11 8+6=1+13
3002 9+6+1=16 8+6=11+3
3003 9+6+2=17 8+6=12+2
3004 9+6+4=19 8+6=13+1
3005 9+6+6=21 8+6=2+12
3006 9+6+7=22 8+6=3+11
3007 9+6+9=24 8+7+1=16
3008 9+6=1+14 8+7+2=17
3009 9+6=11+4 8+7+3=18
3010 9+6=12+3 8+7+6=21
3011 9+6=13+2 8+7+7=22
3012 9+6=14+1 8+7+8=23
3013 9+6=2+13 8+7=1+14
3014 9+6=3+12 8+7=11+4
3015 9+6=4+11 8+7=12+3
3016 9+7+1=17 8+7=13+2
3017 9+7+3=19 8+7=14+1
3018 9+7+5=21 8+7=2+13
3019 9+7+6=22 8+7=3+12
3020 9+7+7=23 8+7=4+11
3021 9+7+9=25 8+8+1=17
3022 9+7=1+15 8+8+2=18
3023 9+7=11+5 8+8+5=21
3024 9+7=12+4 8+8+6=22
3025 9+7=13+3 8+8+7=23
3026 9+7=14+2 8+8+8=24
3027 9+7=15+1 8+8=1+15
3028 9+7=2+14 8+8=11+5
3029 9+7=3+13 8+8=12+4
3030 9+7=4+12 8+8=13+3
3031 9+7=5+11 8+8=14+2
3032 9+9+1=19 8+8=15+1
3033 9+9+3=21 8+8=2+14
3034 9+9+4=22 8+8=3+13
3035 9+9+5=23 8+8=4+12
3036 9+9+6=24 8+8=5+11
3037 9+9+7=25 81=13+68
3038 9+9+9=27 81=14+67
3039 9+9=1+17 81=15+66
3040 9+9=11+7 81=16+65
3041 9+9=12+6 81=17+64
3042 9+9=13+5 81=18+63
3043 9+9=14+4 81=23+58
3044 9+9=15+3 81=24+57
3045 9+9=16+2 81=25+56
3046 9+9=17+1 81=26+55
3047 9+9=2+16 81=27+54
3048 9+9=3+15 81=28+53
3049 9+9=4+14 81=33+48
3050 9+9=5+13 81=34+47
3051 9+9=6+12 81=35+46
3052 9+9=7+11 81=36+45
3053 91=12+79 81=37+44
3054 91=14+77 81=38+43
3055 91=15+76 81=43+38
3056 91=16+75 81=44+37
3057 91=17+74 81=45+36
3058 91=19+72 81=46+35
3059 91=22+69 81=47+34
3060 91=24+67 81=48+33
3061 91=25+66 81=53+28
3062 91=26+65 81=54+27
3063 91=27+64 81=55+26
3064 91=29+62 81=56+25
3065 91=32+59 81=57+24
3066 91=34+57 81=58+23
3067 91=35+56 81=63+18
3068 91=36+55 81=64+17
3069 91=37+54 81=65+16
3070 91=39+52 81=66+15
3071 91=42+49 81=67+14
3072 91=44+47 81=68+13
3073 91=45+46 81=81=81
3074 91=46+45 82=11+71
3075 91=47+44 82=14+68
3076 91=49+42 82=15+67
3077 91=52+39 82=16+66
3078 91=54+37 82=17+65
3079 91=55+36 82=18+64
3080 91=56+35 82=21+61
3081 91=57+34 82=24+58
3082 91=59+32 82=25+57
3083 91=62+29 82=26+56
3084 91=64+27 82=27+55
3085 91=65+26 82=28+54
3086 91=66+25 82=31+51
3087 91=67+24 82=34+48
3088 91=69+22 82=35+47
3089 91=72+19 82=36+46
3090 91=74+17 82=37+45
3091 91=75+16 82=38+44
3092 91=76+15 82=41+41
3093 91=77+14 82=44+38
3094 91=79+12 82=45+37
3095 91=91=91 82=46+36
3096 92=13+79 82=47+35
3097 92=15+77 82=48+34
3098 92=16+76 82=51+31
3099 92=17+75 82=54+28
3100 92=19+73 82=55+27
3101 92=21+71 82=56+26
3102 92=23+69 82=57+25
3103 92=25+67 82=58+24
3104 92=26+66 82=61+21
3105 92=27+65 82=64+18
3106 92=29+63 82=65+17
3107 92=31+61 82=66+16
3108 92=33+59 82=67+15
3109 92=35+57 82=68+14
3110 92=36+56 82=71+11
3111 92=37+55 82=82=82
3112 92=39+53 83=11+72
3113 92=41+51 83=12+71
3114 92=43+49 83=15+68
3115 92=45+47 83=16+67
3116 92=46+46 83=17+66
3117 92=47+45 83=18+65
3118 92=49+43 83=21+62
3119 92=51+41 83=22+61
3120 92=53+39 83=25+58
3121 92=55+37 83=26+57
3122 92=56+36 83=27+56
3123 92=57+35 83=28+55
3124 92=59+33 83=31+52
3125 92=61+31 83=32+51
3126 92=63+29 83=35+48
3127 92=65+27 83=36+47
3128 92=66+26 83=37+46
3129 92=67+25 83=38+45
3130 92=69+23 83=41+42
3131 92=71+21 83=42+41
3132 92=73+19 83=45+38
3133 92=75+17 83=46+37
3134 92=76+16 83=47+36
3135 92=77+15 83=48+35
3136 92=79+13 83=51+32
3137 92=92=92 83=52+31
3138 93=14+79 83=55+28
3139 93=16+77 83=56+27
3140 93=17+76 83=57+26
3141 93=19+74 83=58+25
3142 93=21+72 83=61+22
3143 93=22+71 83=62+21
3144 93=24+69 83=65+18
3145 93=26+67 83=66+17
3146 93=27+66 83=67+16
3147 93=29+64 83=68+15
3148 93=31+62 83=71+12
3149 93=32+61 83=72+11
3150 93=34+59 83=83=83
3151 93=36+57 84=11+73
3152 93=37+56 84=12+72
3153 93=39+54 84=13+71
3154 93=41+52 84=16+68
3155 93=42+51 84=17+67
3156 93=44+49 84=18+66
3157 93=46+47 84=21+63
3158 93=47+46 84=22+62
3159 93=49+44 84=23+61
3160 93=51+42 84=26+58
3161 93=52+41 84=27+57
3162 93=54+39 84=28+56
3163 93=56+37 84=31+53
3164 93=57+36 84=32+52
3165 93=59+34 84=33+51
3166 93=61+32 84=36+48
3167 93=62+31 84=37+47
3168 93=64+29 84=38+46
3169 93=66+27 84=41+43
3170 93=67+26 84=42+42
3171 93=69+24 84=43+41
3172 93=71+22 84=46+38
3173 93=72+21 84=47+37
3174 93=74+19 84=48+36
3175 93=76+17 84=51+33
3176 93=77+16 84=52+32
3177 93=79+14 84=53+31
3178 93=93=93 84=56+28
3179 94=15+79 84=57+27
3180 94=17+77 84=58+26
3181 94=19+75 84=61+23
3182 94=21+73 84=62+22
3183 94=22+72 84=63+21
3184 94=23+71 84=66+18
3185 94=25+69 84=67+17
3186 94=27+67 84=68+16
3187 94=29+65 84=71+13
3188 94=31+63 84=72+12
3189 94=32+62 84=73+11
3190 94=33+61 84=84=84
3191 94=35+59 85=11+74
3192 94=37+57 85=12+73
3193 94=39+55 85=13+72
3194 94=41+53 85=14+71
3195 94=42+52 85=17+68
3196 94=43+51 85=18+67
3197 94=45+49 85=21+64
3198 94=47+47 85=22+63
3199 94=49+45 85=23+62
3200 94=51+43 85=24+61
3201 94=52+42 85=27+58
3202 94=53+41 85=28+57
3203 94=55+39 85=31+54
3204 94=57+37 85=32+53
3205 94=59+35 85=33+52
3206 94=61+33 85=34+51
3207 94=62+32 85=37+48
3208 94=63+31 85=38+47
3209 94=65+29 85=41+44
3210 94=67+27 85=42+43
3211 94=69+25 85=43+42
3212 94=71+23 85=44+41
3213 94=72+22 85=47+38
3214 94=73+21 85=48+37
3215 94=75+19 85=51+34
3216 94=77+17 85=52+33
3217 94=79+15 85=53+32
3218 94=94=94 85=54+31
3219 95=16+79 85=57+28
3220 95=19+76 85=58+27
3221 95=21+74 85=61+24
3222 95=22+73 85=62+23
3223 95=23+72 85=63+22
3224 95=24+71 85=64+21
3225 95=26+69 85=67+18
3226 95=29+66 85=68+17
3227 95=31+64 85=71+14
3228 95=32+63 85=72+13
3229 95=33+62 85=73+12
3230 95=34+61 85=74+11
3231 95=36+59 85=85=85
3232 95=39+56 86=11+75
3233 95=41+54 86=12+74
3234 95=42+53 86=13+73
3235 95=43+52 86=14+72
3236 95=44+51 86=15+71
3237 95=46+49 86=18+68
3238 95=49+46 86=21+65
3239 95=51+44 86=22+64
3240 95=52+43 86=23+63
3241 95=53+42 86=24+62
3242 95=54+41 86=25+61
3243 95=56+39 86=28+58
3244 95=59+36 86=31+55
3245 95=61+34 86=32+54
3246 95=62+33 86=33+53
3247 95=63+32 86=34+52
3248 95=64+31 86=35+51
3249 95=66+29 86=38+48
3250 95=69+26 86=41+45
3251 95=71+24 86=42+44
3252 95=72+23 86=43+43
3253 95=73+22 86=44+42
3254 95=74+21 86=45+41
3255 95=76+19 86=48+38
3256 95=79+16 86=51+35
3257 95=95=95 86=52+34
3258 96=17+79 86=53+33
3259 96=19+77 86=54+32
3260 96=21+75 86=55+31
3261 96=22+74 86=58+28
3262 96=23+73 86=61+25
3263 96=24+72 86=62+24
3264 96=25+71 86=63+23
3265 96=27+69 86=64+22
3266 96=29+67 86=65+21
3267 96=31+65 86=68+18
3268 96=32+64 86=71+15
3269 96=33+63 86=72+14
3270 96=34+62 86=73+13
3271 96=35+61 86=74+12
3272 96=37+59 86=75+11
3273 96=39+57 86=86=86
3274 96=41+55 87=11+76
3275 96=42+54 87=12+75
3276 96=43+53 87=13+74
3277 96=44+52 87=14+73
3278 96=45+51 87=15+72
3279 96=47+49 87=16+71
3280 96=49+47 87=21+66
3281 96=51+45 87=22+65
3282 96=52+44 87=23+64
3283 96=53+43 87=24+63
3284 96=54+42 87=25+62
3285 96=55+41 87=26+61
3286 96=57+39 87=31+56
3287 96=59+37 87=32+55
3288 96=61+35 87=33+54
3289 96=62+34 87=34+53
3290 96=63+33 87=35+52
3291 96=64+32 87=36+51
3292 96=65+31 87=41+46
3293 96=67+29 87=42+45
3294 96=69+27 87=43+44
3295 96=71+25 87=44+43
3296 96=72+24 87=45+42
3297 96=73+23 87=46+41
3298 96=74+22 87=51+36
3299 96=75+21 87=52+35
3300 96=77+19 87=53+34
3301 96=79+17 87=54+33
3302 96=96=96 87=55+32
3303 97=21+76 87=56+31
3304 97=22+75 87=61+26
3305 97=23+74 87=62+25
3306 97=24+73 87=63+24
3307 97=25+72 87=64+23
3308 97=26+71 87=65+22
3309 97=31+66 87=66+21
3310 97=32+65 87=71+16
3311 97=33+64 87=72+15
3312 97=34+63 87=73+14
3313 97=35+62 87=74+13
3314 97=36+61 87=75+12
3315 97=41+56 87=76+11
3316 97=42+55 87=87=87
3317 97=43+54 88=11+77
3318 97=44+53 88=12+76
3319 97=45+52 88=13+75
3320 97=46+51 88=14+74
3321 97=51+46 88=15+73
3322 97=52+45 88=16+72
3323 97=53+44 88=17+71
3324 97=54+43 88=21+67
3325 97=55+42 88=22+66
3326 97=56+41 88=23+65
3327 97=61+36 88=24+64
3328 97=62+35 88=25+63
3329 97=63+34 88=26+62
3330 97=64+33 88=27+61
3331 97=65+32 88=31+57
3332 97=66+31 88=32+56
3333 97=71+26 88=33+55
3334 97=72+25 88=34+54
3335 97=73+24 88=35+53
3336 97=74+23 88=36+52
3337 97=75+22 88=37+51
3338 97=76+21 88=41+47
3339 97=97=97 88=42+46
3340 99=22+77 88=43+45
3341 99=23+76 88=44+44
3342 99=24+75 88=45+43
3343 99=25+74 88=46+42
3344 99=26+73 88=47+41
3345 99=27+72 88=51+37
3346 99=32+67 88=52+36
3347 99=33+66 88=53+35
3348 99=34+65 88=54+34
3349 99=35+64 88=55+33
3350 99=36+63 88=56+32
3351 99=37+62 88=57+31
3352 99=42+57 88=61+27
3353 99=43+56 88=62+26
3354 99=44+55 88=63+25
3355 99=45+54 88=64+24
3356 99=46+53 88=65+23
3357 99=47+52 88=66+22
3358 99=52+47 88=67+21
3359 99=53+46 88=71+17
3360 99=54+45 88=72+16
3361 99=55+44 88=73+15
3362 99=56+43 88=74+14
3363 99=57+42 88=75+13
3364 99=62+37 88=76+12
3365 99=63+36 88=77+11
3366 99=64+35 88=88=88
3367 99=65+34
3368 99=66+33
3369 99=67+32
3370 99=72+27
3371 99=73+26
3372 99=74+25
3373 99=75+24
3374 99=76+23
3375 99=77+22
3376 99=99=99
[0+8=]
gives thus the longest finite sequence of 8-digit integers:
S(8) = 10109811, 10118309,
10118507, 10118606, 10118705, 10118903, 10128409, 10128607, 10128706, 10128904,
10138509, 10138707, 10138905, 10148609, 10148906, 10158709, 10158907, 10178909,
10209812, 10307811, 10309813, 10406811, 10407812, 10409814, 10505811, 10506812,
10507813, 10509815, 10604811, 10605812, 10606813, 10607814, 10609816, 10703811,
10704812, 10705813, 10706814, 10707815, 10709817, 10901811, 10902812, 10903813,
10904814, 10905815, 10906816, 10907817, 10909819, 11011822, 11012823, 11013824,
11014825, 11015826, 11016827, 11018309, 11018507, 11018606, 11018705, 11018903,
11021832, 11022833, 11023834, 11024835, 11025836, 11026837, 11028409, 11028607,
11028706, 11028904, 11031842, 11032843, 11033844, 11034845, 11035846, 11036847,
11038509, 11038707, 11038905, 11041852, 11042853, 11043854, 11044855, 11045856,
11046857, 11048609, 11048906, 11051862, 11052863, 11053864, 11054865, 11055866,
11056867, 11058709, 11058907, 11061872, 11062873, 11063874, 11064875, 11065876,
11066877, 11078909, 11810109, 11810307, 11810406, 11810505, 11810604, 11810703,
11810901, 11811811, 11820207, 11820306, 11820405, 11820504, 11820603, 11820702,
11830107, 11830206, 11830305, 11830404, 11830503, 11830602, 11830701, 11840106,
11840205, 11840304, 11840403, 11840502, 11840601, 11850105, 11850204, 11850303,
11850402, 11850501, 11860104, 11860203, 11860302, 11860401, 11870103, 11870202,
11870301, 11890101, 12011823, 12012824, 12013825, 12014826, 12015827, 12017829,
12018409, 12018607, 12018706, 12018904, 12019831, 12021833, 12022834, 12023835,
12024836, 12025837, 12027839, 12028509, 12028707, 12028905, 12029841, 12031843,
12032844, 12033845, 12034846, 12035847, 12037849, 12038609, 12038906, 12039851,
12041853, 12042854, 12043855, 12044856, 12045857, 12047859, 12048709, 12048907,
12049861, 12051863, 12052864, 12053865, 12054866, 12055867, 12057869, 12059871,
12061873, 12062874, 12063875, 12064876, 12065877, 12067879, 12068909, 12079891,
12810209, 12810407, 12810506, 12810605, 12810704, 12810902, 12812812, 12820109,
12820307, 12820406, 12820505, 12820604, 12820703, 12820901, 12830207, 12830306,
12830405, 12830504, 12830603, 12830702, 12840107, 12840206, 12840305, 12840404,
12840503, 12840602, 12840701, 12850106, 12850205, 12850304, 12850403, 12850502,
12850601, 12860105, 12860204, 12860303, 12860402, 12860501, 12870104, 12870203,
12870302, 12870401, 12890102, 12890201, 13011824, 13012825, 13013826, 13014827,
13016829, 13018509, 13018707, 13018905, 13019832, 13021834, 13022835, 13023836,
13024837, 13026839, 13028609, 13028906, 13029842, 13031844, 13032845, 13033846,
13034847, 13036849, 13038709, 13038907, 13039852, 13041854, 13042855, 13043856,
13044857, 13046859, 13049862, 13051864, 13052865, 13053866, 13054867, 13056869,
13058909, 13059872, 13061874, 13062875, 13063876, 13064877, 13066879, 13079892,
13810309, 13810507, 13810606, 13810705, 13810903, 13813813, 13820209, 13820407,
13820506, 13820605, 13820704, 13820902, 13830109, 13830307, 13830406, 13830505,
13830604, 13830703, 13830901, 13840207, 13840306, 13840405, 13840504, 13840603,
13840702, 13850107, 13850206, 13850305, 13850404, 13850503, 13850602, 13850701,
13860106, 13860205, 13860304, 13860403, 13860502, 13860601, 13870105, 13870204,
13870303, 13870402, 13870501, 13890103, 13890202, 13890301, 14011825, 14012826,
14013827, 14015829, 14017831, 14018609, 14018906, 14019833, 14021835, 14022836,
14023837, 14025839, 14027841, 14028709, 14028907, 14029843, 14031845, 14032846,
14033847, 14035849, 14037851, 14039853, 14041855, 14042856, 14043857, 14045859,
14047861, 14048909, 14049863, 14051865, 14052866, 14053867, 14055869, 14057871,
14059873, 14061875, 14062876, 14063877, 14065879, 14077891, 14079893, 14810409,
14810607, 14810706, 14810904, 14814814, 14820309, 14820507, 14820606, 14820705,
14820903, 14830209, 14830407, 14830506, 14830605, 14830704, 14830902, 14840109,
14840307, 14840406, 14840505, 14840604, 14840703, 14840901, 14850207, 14850306,
14850405, 14850504, 14850603, 14850702, 14860107, 14860206, 14860305, 14860404,
14860503, 14860602, 14860701, 14870106, 14870205, 14870304, 14870403, 14870502,
14870601, 14890104, 14890203, 14890302, 14890401, 15011826, 15012827, 15014829,
15016831, 15017832, 15018709, 15018907, 15019834, 15021836, 15022837, 15024839,
15026841, 15027842, 15029844, 15031846, 15032847, 15034849, 15036851, 15037852,
15038909, 15039854, 15041856, 15042857, 15044859, 15046861, 15047862, 15049864,
15051866, 15052867, 15054869, 15056871, 15057872, 15059874, 15061876, 15062877,
15064879, 15076891, 15077892, 15079894, 15810509, 15810707, 15810905, 15815815,
15820409, 15820607, 15820706, 15820904, 15830309, 15830507, 15830606, 15830705,
15830903, 15840209, 15840407, 15840506, 15840605, 15840704, 15840902, 15850109,
15850307, 15850406, 15850505, 15850604, 15850703, 15850901, 15860207, 15860306,
15860405, 15860504, 15860603, 15860702, 15870107, 15870206, 15870305, 15870404,
15870503, 15870602, 15870701, 15890105, 15890204, 15890303, 15890402, 15890501,
16011827, 16013829, 16015831, 16016832, 16017833, 16019835, 16021837, 16023839,
16025841, 16026842, 16027843, 16028909, 16029845, 16031847, 16033849, 16035851,
16036852, 16037853, 16039855, 16041857, 16043859, 16045861, 16046862, 16047863,
16049865, 16051867, 16053869, 16055871, 16056872, 16057873, 16059875, 16061877,
16063879, 16075891, 16076892, 16077893, 16079895, 16810609, 16810906, 16816816,
16820509, 16820707, 16820905, 16830409, 16830607, 16830706, 16830904, 16840309,
16840507, 16840606, 16840705, 16840903, 16850209, 16850407, 16850506, 16850605,
16850704, 16850902, 16860109, 16860307, 16860406, 16860505, 16860604, 16860703,
16860901, 16870207, 16870306, 16870405, 16870504, 16870603, 16870702, 16890106,
16890205, 16890304, 16890403, 16890502, 16890601, 17012829, 17014831, 17015832,
17016833, 17017834, 17018909, 17019836, 17022839, 17024841, 17025842, 17026843,
17027844, 17029846, 17032849, 17034851, 17035852, 17036853, 17037854, 17039856,
17042859, 17044861, 17045862, 17046863, 17047864, 17049866, 17052869, 17054871,
17055872, 17056873, 17057874, 17059876, 17062879, 17074891, 17075892, 17076893,
17077894, 17079896, 17810709, 17810907, 17817817, 17820609, 17820906, 17830509,
17830707, 17830905, 17840409, 17840607, 17840706, 17840904, 17850309, 17850507,
17850606, 17850705, 17850903, 17860209, 17860407, 17860506, 17860605, 17860704,
17860902, 17870109, 17870307, 17870406, 17870505, 17870604, 17870703, 17870901,
17890107, 17890206, 17890305, 17890404, 17890503, 17890602, 17890701, 19012831,
19013832, 19014833, 19015834, 19016835, 19017836, 19022841, 19023842, 19024843,
19025844, 19026845, 19027846, 19032851, 19033852, 19034853, 19035854, 19036855,
19037856, 19042861, 19043862, 19044863, 19045864, 19046865, 19047866, 19052871,
19053872, 19054873, 19055874, 19056875, 19057876, 19072891, 19073892, 19074893,
19075894, 19076895, 19077896, 19810909, 19819819, 19830709, 19830907, 19840609,
19840906, 19850509, 19850707, 19850905, 19860409, 19860607, 19860706, 19860904,
19870309, 19870507, 19870606, 19870705, 19870903, 19890109, 19890307, 19890406,
19890505, 19890604, 19890703, 19890901, 20109812, 20118409, 20118607, 20118706,
20118904, 20128509, 20128707, 20128905, 20138609, 20138906, 20148709, 20148907,
20168909, 20207811, 20209813, 20306811, 20307812, 20309814, 20405811, 20406812,
20407813, 20409815, 20504811, 20505812, 20506813, 20507814, 20509816, 20603811,
20604812, 20605813, 20606814, 20607815, 20609817, 20702811, 20703812, 20704813,
20705814, 20706815, 20707816, 20901812, 20902813, 20903814, 20904815, 20905816,
20906817, 21011832, 21012833, 21013834, 21014835, 21015836, 21016837, 21021842,
21022843, 21023844, 21024845, 21025846, 21026847, 21031852, 21032853, 21033854,
21034855, 21035856, 21036857, 21041862, 21042863, 21043864, 21044865, 21045866,
21046867, 21051872, 21052873, 21053874, 21054875, 21055876, 21056877, 21071892,
21072893, 21073894, 21074895, 21075896, 21076897, 21821821, 21830909, 21850709,
21850907, 21860609, 21860906, 21870509, 21870707, 21870905, 21890309, 21890507,
21890606, 21890705, 21890903, 22011833, 22012834, 22013835, 22014836, 22015837,
22017839, 22019841, 22021843, 22022844, 22023845, 22024846, 22025847, 22027849,
22029851, 22031853, 22032854, 22033855, 22034856, 22035857, 22037859, 22039861,
22041863, 22042864, 22043865, 22044866, 22045867, 22047869, 22049871, 22051873,
22052874, 22053875, 22054876, 22055877, 22057879, 22069891, 22071893, 22072894,
22073895, 22074896, 22075897, 22077899, 22811011, 22822822, 22840909, 22860709,
22860907, 22870609, 22870906, 22890409, 22890607, 22890706, 22890904, 23011834,
23012835, 23013836, 23014837, 23016839, 23019842, 23021844, 23022845, 23023846,
23024847, 23026849, 23029852, 23031854, 23032855, 23033856, 23034857, 23036859,
23039862, 23041864, 23042865, 23043866, 23044867, 23046869, 23049872, 23051874,
23052875, 23053876, 23054877, 23056879, 23069892, 23071894, 23072895, 23073896,
23074897, 23076899, 23811012, 23812011, 23823823, 23850909, 23870709, 23870907,
23890509, 23890707, 23890905, 24011835, 24012836, 24013837, 24015839, 24017841,
24019843, 24021845, 24022846, 24023847, 24025849, 24027851, 24029853, 24031855,
24032856, 24033857, 24035859, 24037861, 24039863, 24041865, 24042866, 24043867,
24045869, 24047871, 24049873, 24051875, 24052876, 24053877, 24055879, 24067891,
24069893, 24071895, 24072896, 24073897, 24075899, 24811013, 24812012, 24813011,
24824824, 24860909, 24890609, 24890906, 25011836, 25012837, 25014839, 25016841,
25017842, 25019844, 25021846, 25022847, 25024849, 25026851, 25027852, 25029854,
25031856, 25032857, 25034859, 25036861, 25037862, 25039864, 25041866, 25042867,
25044869, 25046871, 25047872, 25049874, 25051876, 25052877, 25054879, 25066891,
25067892, 25069894, 25071896, 25072897, 25074899, 25811014, 25812013, 25813012,
25814011, 25825825, 25870909, 25890709, 25890907, 26011837, 26013839, 26015841,
26016842, 26017843, 26019845, 26021847, 26023849, 26025851, 26026852, 26027853,
26029855, 26031857, 26033859, 26035861, 26036862, 26037863, 26039865, 26041867,
26043869, 26045871, 26046872, 26047873, 26049875, 26051877, 26053879, 26065891,
26066892, 26067893, 26069895, 26071897, 26073899, 26811015, 26812014, 26813013,
26814012, 26815011, 26826826, 27012839, 27014841, 27015842, 27016843, 27017844,
27019846, 27022849, 27024851, 27025852, 27026853, 27027854, 27029856, 27032859,
27034861, 27035862, 27036863, 27037864, 27039866, 27042869, 27044871, 27045872,
27046873, 27047874, 27049876, 27052879, 27064891, 27065892, 27066893, 27067894,
27069896, 27072899, 27811016, 27812015, 27813014, 27814013, 27815012, 27816011,
27827827, 27890909, 29012841, 29013842, 29014843, 29015844, 29016845, 29017846,
29022851, 29023852, 29024853, 29025854, 29026855, 29027856, 29032861, 29033862,
29034863, 29035864, 29036865, 29037866, 29042871, 29043872, 29044873, 29045874,
29046875, 29047876, 29062891, 29063892, 29064893, 29065894, 29066895, 29067896,
29812017, 29813016, 29814015, 29815014, 29816013, 29817012, 29829829, 30107811,
30109813, 30118509, 30118707, 30118905, 30128609, 30128906, 30138709, 30138907,
30158909, 30206811, 30207812, 30209814, 30305811, 30306812, 30307813, 30309815,
30404811, 30405812, 30406813, 30407814, 30409816, 30503811, 30504812, 30505813,
30506814, 30507815, 30509817, 30602811, 30603812, 30604813, 30605814, 30606815,
30607816, 30701811, 30702812, 30703813, 30704814, 30705815, 30706816, 30707817,
30709819, 30901813, 30902814, 30903815, 30904816, 30905817, 30907819, 30909821,
30981011, 30981101, 31011842, 31012843, 31013844, 31014845, 31015846, 31016847,
31021852, 31022853, 31023854, 31024855, 31025856, 31026857, 31031862, 31032863,
31033864, 31034865, 31035866, 31036867, 31041872, 31042873, 31043874, 31044875,
31045876, 31046877, 31061892, 31062893, 31063894, 31064895, 31065896, 31066897,
31812019, 31814017, 31815016, 31816015, 31817014, 31819012, 31831831, 32011843,
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77821056, 77822055, 77823054, 77824053, 77825052, 77826051, 77831046, 77832045,
77833044, 77834043, 77835042, 77836041, 77841036, 77842035, 77843034, 77844033,
77845032, 77846031, 77851026, 77852025, 77853024, 77854023, 77855022, 77856021,
77861016, 77862015, 77863014, 77864013, 77865012, 77866011, 77877877, 79012891,
79013892, 79014893, 79015894, 79016895, 79017896, 79812067, 79813066, 79814065,
79815064, 79816063, 79817062, 79822057, 79823056, 79824055, 79825054, 79826053,
79827052, 79832047, 79833046, 79834045, 79835044, 79836043, 79837042, 79842037,
79843036, 79844035, 79845034, 79846033, 79847032, 79852027, 79853026, 79854025,
79855024, 79856023, 79857022, 79862017, 79863016, 79864015, 79865014, 79866013,
79867012, 79879879, 90101811, 90102812, 90103813, 90104814, 90105815, 90106816,
90107817, 90109819, 90201812, 90202813, 90203814, 90204815, 90205816, 90206817,
90301813, 90302814, 90303815, 90304816, 90305817, 90307819, 90309821, 90381011,
90381101, 90401814, 90402815, 90403816, 90404817, 90406819, 90409822, 90481012,
90481102, 90481201, 90482011, 90501815, 90502816, 90503817, 90505819, 90507821,
90509823, 90581013, 90581103, 90581202, 90581301, 90582012, 90583011, 90601816,
90602817, 90604819, 90606821, 90607822, 90609824, 90681014, 90681104, 90681203,
90681302, 90681401, 90682013, 90683012, 90684011, 90701817, 90703819, 90705821,
90706822, 90707823, 90709825, 90781015, 90781105, 90781204, 90781303, 90781402,
90781501, 90782014, 90783013, 90784012, 90785011, 90901819, 90903821, 90904822,
90905823, 90906824, 90907825, 90909827, 90981017, 90981107, 90981206, 90981305,
90981404, 90981503, 90981602, 90981701, 90982016, 90983015, 90984014, 90985013,
90986012, 90987011, 91812079, 91814077, 91815076, 91816075, 91817074, 91819072,
91822069, 91824067, 91825066, 91826065, 91827064, 91829062, 91832059, 91834057,
91835056, 91836055, 91837054, 91839052, 91842049, 91844047, 91845046, 91846045,
91847044, 91849042, 91852039, 91854037, 91855036, 91856035, 91857034, 91859032,
91862029, 91864027, 91865026, 91866025, 91867024, 91869022, 91872019, 91874017,
91875016, 91876015, 91877014, 91879012, 91891891, 92813079, 92815077, 92816076,
92817075, 92819073, 92821071, 92823069, 92825067, 92826066, 92827065, 92829063,
92831061, 92833059, 92835057, 92836056, 92837055, 92839053, 92841051, 92843049,
92845047, 92846046, 92847045, 92849043, 92851041, 92853039, 92855037, 92856036,
92857035, 92859033, 92861031, 92863029, 92865027, 92866026, 92867025, 92869023,
92871021, 92873019, 92875017, 92876016, 92877015, 92879013, 92892892, 93814079,
93816077, 93817076, 93819074, 93821072, 93822071, 93824069, 93826067, 93827066,
93829064, 93831062, 93832061, 93834059, 93836057, 93837056, 93839054, 93841052,
93842051, 93844049, 93846047, 93847046, 93849044, 93851042, 93852041, 93854039,
93856037, 93857036, 93859034, 93861032, 93862031, 93864029, 93866027, 93867026,
93869024, 93871022, 93872021, 93874019, 93876017, 93877016, 93879014, 93893893,
94815079, 94817077, 94819075, 94821073, 94822072, 94823071, 94825069, 94827067,
94829065, 94831063, 94832062, 94833061, 94835059, 94837057, 94839055, 94841053,
94842052, 94843051, 94845049, 94847047, 94849045, 94851043, 94852042, 94853041,
94855039, 94857037, 94859035, 94861033, 94862032, 94863031, 94865029, 94867027,
94869025, 94871023, 94872022, 94873021, 94875019, 94877017, 94879015, 94894894,
95816079, 95819076, 95821074, 95822073, 95823072, 95824071, 95826069, 95829066,
95831064, 95832063, 95833062, 95834061, 95836059, 95839056, 95841054, 95842053,
95843052, 95844051, 95846049, 95849046, 95851044, 95852043, 95853042, 95854041,
95856039, 95859036, 95861034, 95862033, 95863032, 95864031, 95866029, 95869026,
95871024, 95872023, 95873022, 95874021, 95876019, 95879016, 95895895, 96817079,
96819077, 96821075, 96822074, 96823073, 96824072, 96825071, 96827069, 96829067,
96831065, 96832064, 96833063, 96834062, 96835061, 96837059, 96839057, 96841055,
96842054, 96843053, 96844052, 96845051, 96847049, 96849047, 96851045, 96852044,
96853043, 96854042, 96855041, 96857039, 96859037, 96861035, 96862034, 96863033,
96864032, 96865031, 96867029, 96869027, 96871025, 96872024, 96873023, 96874022,
96875021, 96877019, 96879017, 96896896, 97821076, 97822075, 97823074, 97824073,
97825072, 97826071, 97831066, 97832065, 97833064, 97834063, 97835062, 97836061,
97841056, 97842055, 97843054, 97844053, 97845052, 97846051, 97851046, 97852045,
97853044, 97854043, 97855042, 97856041, 97861036, 97862035, 97863034, 97864033,
97865032, 97866031, 97871026, 97872025, 97873024, 97874023, 97875022, 97876021,
97897897, 99822077, 99823076, 99824075, 99825074, 99826073, 99827072, 99832067,
99833066, 99834065, 99835064, 99836063, 99837062, 99842057, 99843056, 99844055,
99845054, 99846053, 99847052, 99852047, 99853046, 99854045, 99855044, 99856043,
99857042, 99862037, 99863036, 99864035, 99865034, 99866033, 99867032, 99872027,
99873026, 99874025, 99875024, 99876023, 99877022, 99899899.
Note that for symmetry reasons the code [0=8+] would also produce a maximum of 3376 terms:
S’(8) = 11011011, 11018189,
11018387, 11018486, 11018585, 11018684, 11018783, 11018981, 11028287, 11028386,
11028485, 11028584, 11028683, 11028782, 11038187, 11038286, 11038385, 11038484,
11038583, 11038682, 11038781, 11048186, 11048285, 11048384, 11048483, 11048582,
11048681, 11058185, 11058284, 11058383, 11058482, 11058581, 11068184, 11068283,
11068382, 11068481, 11078183, 11078282, 11078381, 11098181, 11810389, 11810587,
11810686, 11810785, 11810983, 11811022, 11812023, 11813024, 11814025, 11815026,
11816027, 11820489, 11820687, 11820786, 11820984, 11821032, 11822033, 11823034,
11824035, 11825036, 11826037, 11830589, 11830787, 11830985, 11831042, 11832043,
11833044, 11834045, 11835046, 11836047, 11840689, 11840986, 11841052, 11842053,
11843054, 11844055, 11845056, 11846057, 11850789, 11850987, 11851062, 11852063,
11853064, 11854065, 11855066, 11856067, 11861072, 11862073, 11863074, 11864075,
11865076, 11866077, 11870989, 12012012, 12018289, 12018487, 12018586, 12018685,
12018784, 12018982, 12028189, 12028387, 12028486, 12028585, 12028684, 12028783,
12028981, 12038287, 12038386, 12038485, 12038584, 12038683, 12038782, 12048187,
12048286, 12048385, 12048484, 12048583, 12048682, 12048781, 12058186, 12058285,
12058384, 12058483, 12058582, 12058681, 12068185, 12068284, 12068383, 12068482,
12068581, 12078184, 12078283, 12078382, 12078481, 12098182, 12098281, 12810489,
12810687, 12810786, 12810984, 12811023, 12812024, 12813025, 12814026, 12815027,
12817029, 12819031, 12820589, 12820787, 12820985, 12821033, 12822034, 12823035,
12824036, 12825037, 12827039, 12829041, 12830689, 12830986, 12831043, 12832044,
12833045, 12834046, 12835047, 12837049, 12839051, 12840789, 12840987, 12841053,
12842054, 12843055, 12844056, 12845057, 12847059, 12849061, 12851063, 12852064,
12853065, 12854066, 12855067, 12857069, 12859071, 12860989, 12861073, 12862074,
12863075, 12864076, 12865077, 12867079, 12879091, 13013013, 13018389, 13018587,
13018686, 13018785, 13018983, 13028289, 13028487, 13028586, 13028685, 13028784,
13028982, 13038189, 13038387, 13038486, 13038585, 13038684, 13038783, 13038981,
13048287, 13048386, 13048485, 13048584, 13048683, 13048782, 13058187, 13058286,
13058385, 13058484, 13058583, 13058682, 13058781, 13068186, 13068285, 13068384,
13068483, 13068582, 13068681, 13078185, 13078284, 13078383, 13078482, 13078581,
13098183, 13098282, 13098381, 13810589, 13810787, 13810985, 13811024, 13812025,
13813026, 13814027, 13816029, 13819032, 13820689, 13820986, 13821034, 13822035,
13823036, 13824037, 13826039, 13829042, 13830789, 13830987, 13831044, 13832045,
13833046, 13834047, 13836049, 13839052, 13841054, 13842055, 13843056, 13844057,
13846059, 13849062, 13850989, 13851064, 13852065, 13853066, 13854067, 13856069,
13859072, 13861074, 13862075, 13863076, 13864077, 13866079, 13879092, 14014014,
14018489, 14018687, 14018786, 14018984, 14028389, 14028587, 14028686, 14028785,
14028983, 14038289, 14038487, 14038586, 14038685, 14038784, 14038982, 14048189,
14048387, 14048486, 14048585, 14048684, 14048783, 14048981, 14058287, 14058386,
14058485, 14058584, 14058683, 14058782, 14068187, 14068286, 14068385, 14068484,
14068583, 14068682, 14068781, 14078186, 14078285, 14078384, 14078483, 14078582,
14078681, 14098184, 14098283, 14098382, 14098481, 14810689, 14810986, 14811025,
14812026, 14813027, 14815029, 14817031, 14819033, 14820789, 14820987, 14821035,
14822036, 14823037, 14825039, 14827041, 14829043, 14831045, 14832046, 14833047,
14835049, 14837051, 14839053, 14840989, 14841055, 14842056, 14843057, 14845059,
14847061, 14849063, 14851065, 14852066, 14853067, 14855069, 14857071, 14859073,
14861075, 14862076, 14863077, 14865079, 14877091, 14879093, 15015015, 15018589,
15018787, 15018985, 15028489, 15028687, 15028786, 15028984, 15038389, 15038587,
15038686, 15038785, 15038983, 15048289, 15048487, 15048586, 15048685, 15048784,
15048982, 15058189, 15058387, 15058486, 15058585, 15058684, 15058783, 15058981,
15068287, 15068386, 15068485, 15068584, 15068683, 15068782, 15078187, 15078286,
15078385, 15078484, 15078583, 15078682, 15078781, 15098185, 15098284, 15098383,
15098482, 15098581, 15810789, 15810987, 15811026, 15812027, 15814029, 15816031,
15817032, 15819034, 15821036, 15822037, 15824039, 15826041, 15827042, 15829044,
15830989, 15831046, 15832047, 15834049, 15836051, 15837052, 15839054, 15841056,
15842057, 15844059, 15846061, 15847062, 15849064, 15851066, 15852067, 15854069,
15856071, 15857072, 15859074, 15861076, 15862077, 15864079, 15876091, 15877092,
15879094, 16016016, 16018689, 16018986, 16028589, 16028787, 16028985, 16038489,
16038687, 16038786, 16038984, 16048389, 16048587, 16048686, 16048785, 16048983,
16058289, 16058487, 16058586, 16058685, 16058784, 16058982, 16068189, 16068387,
16068486, 16068585, 16068684, 16068783, 16068981, 16078287, 16078386, 16078485,
16078584, 16078683, 16078782, 16098186, 16098285, 16098384, 16098483, 16098582,
16098681, 16811027, 16813029, 16815031, 16816032, 16817033, 16819035, 16820989,
16821037, 16823039, 16825041, 16826042, 16827043, 16829045, 16831047, 16833049,
16835051, 16836052, 16837053, 16839055, 16841057, 16843059, 16845061, 16846062,
16847063, 16849065, 16851067, 16853069, 16855071, 16856072, 16857073, 16859075,
16861077, 16863079, 16875091, 16876092, 16877093, 16879095, 17017017, 17018789,
17018987, 17028689, 17028986, 17038589, 17038787, 17038985, 17048489, 17048687,
17048786, 17048984, 17058389, 17058587, 17058686, 17058785, 17058983, 17068289,
17068487, 17068586, 17068685, 17068784, 17068982, 17078189, 17078387, 17078486,
17078585, 17078684, 17078783, 17078981, 17098187, 17098286, 17098385, 17098484,
17098583, 17098682, 17098781, 17810989, 17812029, 17814031, 17815032, 17816033,
17817034, 17819036, 17822039, 17824041, 17825042, 17826043, 17827044, 17829046,
17832049, 17834051, 17835052, 17836053, 17837054, 17839056, 17842059, 17844061,
17845062, 17846063, 17847064, 17849066, 17852069, 17854071, 17855072, 17856073,
17857074, 17859076, 17862079, 17874091, 17875092, 17876093, 17877094, 17879096,
18110389, 18110587, 18110686, 18110785, 18110983, 18120489, 18120687, 18120786,
18120984, 18130589, 18130787, 18130985, 18140689, 18140986, 18150789, 18150987,
18170989, 18189011, 18289012, 18387011, 18389013, 18486011, 18487012, 18489014,
18585011, 18586012, 18587013, 18589015, 18684011, 18685012, 18686013, 18687014,
18689016, 18783011, 18784012, 18785013, 18786014, 18787015, 18789017, 18981011,
18982012, 18983013, 18984014, 18985015, 18986016, 18987017, 18989019, 19018989,
19019019, 19038789, 19038987, 19048689, 19048986, 19058589, 19058787, 19058985,
19068489, 19068687, 19068786, 19068984, 19078389, 19078587, 19078686, 19078785,
19078983, 19098189, 19098387, 19098486, 19098585, 19098684, 19098783, 19098981,
19812031, 19813032, 19814033, 19815034, 19816035, 19817036, 19822041, 19823042,
19824043, 19825044, 19826045, 19827046, 19832051, 19833052, 19834053, 19835054,
19836055, 19837056, 19842061, 19843062, 19844063, 19845064, 19846065, 19847066,
19852071, 19853072, 19854073, 19855074, 19856075, 19857076, 19872091, 19873092,
19874093, 19875094, 19876095, 19877096, 21021021, 21038989, 21058789, 21058987,
21068689, 21068986, 21078589, 21078787, 21078985, 21098389, 21098587, 21098686,
21098785, 21098983, 21811032, 21812033, 21813034, 21814035, 21815036, 21816037,
21821042, 21822043, 21823044, 21824045, 21825046, 21826047, 21831052, 21832053,
21833054, 21834055, 21835056, 21836057, 21841062, 21842063, 21843064, 21844065,
21845066, 21846067, 21851072, 21852073, 21853074, 21854075, 21855076, 21856077,
21871092, 21872093, 21873094, 21874095, 21875096, 21876097, 22011811, 22022022,
22048989, 22068789, 22068987, 22078689, 22078986, 22098489, 22098687, 22098786,
22098984, 22811033, 22812034, 22813035, 22814036, 22815037, 22817039, 22819041,
22821043, 22822044, 22823045, 22824046, 22825047, 22827049, 22829051, 22831053,
22832054, 22833055, 22834056, 22835057, 22837059, 22839061, 22841063, 22842064,
22843065, 22844066, 22845067, 22847069, 22849071, 22851073, 22852074, 22853075,
22854076, 22855077, 22857079, 22869091, 22871093, 22872094, 22873095, 22874096,
22875097, 22877099, 23011812, 23012811, 23023023, 23058989, 23078789, 23078987,
23098589, 23098787, 23098985, 23811034, 23812035, 23813036, 23814037, 23816039,
23819042, 23821044, 23822045, 23823046, 23824047, 23826049, 23829052, 23831054,
23832055, 23833056, 23834057, 23836059, 23839062, 23841064, 23842065, 23843066,
23844067, 23846069, 23849072, 23851074, 23852075, 23853076, 23854077, 23856079,
23869092, 23871094, 23872095, 23873096, 23874097, 23876099, 24011813, 24012812,
24013811, 24024024, 24068989, 24098689, 24098986, 24811035, 24812036, 24813037,
24815039, 24817041, 24819043, 24821045, 24822046, 24823047, 24825049, 24827051,
24829053, 24831055, 24832056, 24833057, 24835059, 24837061, 24839063, 24841065,
24842066, 24843067, 24845069, 24847071, 24849073, 24851075, 24852076, 24853077,
24855079, 24867091, 24869093, 24871095, 24872096, 24873097, 24875099, 25011814,
25012813, 25013812, 25014811, 25025025, 25078989, 25098789, 25098987, 25811036,
25812037, 25814039, 25816041, 25817042, 25819044, 25821046, 25822047, 25824049,
25826051, 25827052, 25829054, 25831056, 25832057, 25834059, 25836061, 25837062,
25839064, 25841066, 25842067, 25844069, 25846071, 25847072, 25849074, 25851076,
25852077, 25854079, 25866091, 25867092, 25869094, 25871096, 25872097, 25874099,
26011815, 26012814, 26013813, 26014812, 26015811, 26026026, 26811037, 26813039,
26815041, 26816042, 26817043, 26819045, 26821047, 26823049, 26825051, 26826052,
26827053, 26829055, 26831057, 26833059, 26835061, 26836062, 26837063, 26839065,
26841067, 26843069, 26845071, 26846072, 26847073, 26849075, 26851077, 26853079,
26865091, 26866092, 26867093, 26869095, 26871097, 26873099, 27011816, 27012815,
27013814, 27014813, 27015812, 27016811, 27027027, 27098989, 27812039, 27814041,
27815042, 27816043, 27817044, 27819046, 27822049, 27824051, 27825052, 27826053,
27827054, 27829056, 27832059, 27834061, 27835062, 27836063, 27837064, 27839066,
27842069, 27844071, 27845072, 27846073, 27847074, 27849076, 27852079, 27864091,
27865092, 27866093, 27867094, 27869096, 27872099, 28110489, 28110687, 28110786,
28110984, 28120589, 28120787, 28120985, 28130689, 28130986, 28140789, 28140987,
28160989, 28189012, 28287011, 28289013, 28386011, 28387012, 28389014, 28485011,
28486012, 28487013, 28489015, 28584011, 28585012, 28586013, 28587014, 28589016,
28683011, 28684012, 28685013, 28686014, 28687015, 28689017, 28782011, 28783012,
28784013, 28785014, 28786015, 28787016, 28981012, 28982013, 28983014, 28984015,
28985016, 28986017, 29012817, 29013816, 29014815, 29015814, 29016813, 29017812,
29029029, 29812041, 29813042, 29814043, 29815044, 29816045, 29817046, 29822051,
29823052, 29824053, 29825054, 29826055, 29827056, 29832061, 29833062, 29834063,
29835064, 29836065, 29837066, 29842071, 29843072, 29844073, 29845074, 29846075,
29847076, 29862091, 29863092, 29864093, 29865094, 29866095, 29867096, 31012819,
31014817, 31015816, 31016815, 31017814, 31019812, 31031031, 31811042, 31812043,
31813044, 31814045, 31815046, 31816047, 31821052, 31822053, 31823054, 31824055,
31825056, 31826057, 31831062, 31832063, 31833064, 31834065, 31835066, 31836067,
31841072, 31842073, 31843074, 31844075, 31845076, 31846077, 31861092, 31862093,
31863094, 31864095, 31865096, 31866097, 32011821, 32013819, 32015817, 32016816,
32017815, 32019813, 32021811, 32032032, 32811043, 32812044, 32813045, 32814046,
32815047, 32817049, 32819051, 32821053, 32822054, 32823055, 32824056, 32825057,
32827059, 32829061, 32831063, 32832064, 32833065, 32834066, 32835067, 32837069,
32839071, 32841073, 32842074, 32843075, 32844076, 32845077, 32847079, 32859091,
32861093, 32862094, 32863095, 32864096, 32865097, 32867099, 33011822, 33012821,
33014819, 33016817, 33017816, 33019814, 33021812, 33022811, 33033033, 33811044,
33812045, 33813046, 33814047, 33816049, 33819052, 33821054, 33822055, 33823056,
33824057, 33826059, 33829062, 33831064, 33832065, 33833066, 33834067, 33836069,
33839072, 33841074, 33842075, 33843076, 33844077, 33846079, 33859092, 33861094,
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79025854, 79026853, 79027852, 79032847, 79033846, 79034845, 79035844, 79036843,
79037842, 79042837, 79043836, 79044835, 79045834, 79046833, 79047832, 79052827,
79053826, 79054825, 79055824, 79056823, 79057822, 79062817, 79063816, 79064815,
79065814, 79066813, 79067812, 79079079, 79812091, 79813092, 79814093, 79815094,
79816095, 79817096, 91012879, 91014877, 91015876, 91016875, 91017874, 91019872,
91022869, 91024867, 91025866, 91026865, 91027864, 91029862, 91032859, 91034857,
91035856, 91036855, 91037854, 91039852, 91042849, 91044847, 91045846, 91046845,
91047844, 91049842, 91052839, 91054837, 91055836, 91056835, 91057834, 91059832,
91062829, 91064827, 91065826, 91066825, 91067824, 91069822, 91072819, 91074817,
91075816, 91076815, 91077814, 91079812, 91091091, 92013879, 92015877, 92016876,
92017875, 92019873, 92021871, 92023869, 92025867, 92026866, 92027865, 92029863,
92031861, 92033859, 92035857, 92036856, 92037855, 92039853, 92041851, 92043849,
92045847, 92046846, 92047845, 92049843, 92051841, 92053839, 92055837, 92056836,
92057835, 92059833, 92061831, 92063829, 92065827, 92066826, 92067825, 92069823,
92071821, 92073819, 92075817, 92076816, 92077815, 92079813, 92092092, 93014879,
93016877, 93017876, 93019874, 93021872, 93022871, 93024869, 93026867, 93027866,
93029864, 93031862, 93032861, 93034859, 93036857, 93037856, 93039854, 93041852,
93042851, 93044849, 93046847, 93047846, 93049844, 93051842, 93052841, 93054839,
93056837, 93057836, 93059834, 93061832, 93062831, 93064829, 93066827, 93067826,
93069824, 93071822, 93072821, 93074819, 93076817, 93077816, 93079814, 93093093,
94015879, 94017877, 94019875, 94021873, 94022872, 94023871, 94025869, 94027867,
94029865, 94031863, 94032862, 94033861, 94035859, 94037857, 94039855, 94041853,
94042852, 94043851, 94045849, 94047847, 94049845, 94051843, 94052842, 94053841,
94055839, 94057837, 94059835, 94061833, 94062832, 94063831, 94065829, 94067827,
94069825, 94071823, 94072822, 94073821, 94075819, 94077817, 94079815, 94094094,
95016879, 95019876, 95021874, 95022873, 95023872, 95024871, 95026869, 95029866,
95031864, 95032863, 95033862, 95034861, 95036859, 95039856, 95041854, 95042853,
95043852, 95044851, 95046849, 95049846, 95051844, 95052843, 95053842, 95054841,
95056839, 95059836, 95061834, 95062833, 95063832, 95064831, 95066829, 95069826,
95071824, 95072823, 95073822, 95074821, 95076819, 95079816, 95095095, 96017879,
96019877, 96021875, 96022874, 96023873, 96024872, 96025871, 96027869, 96029867,
96031865, 96032864, 96033863, 96034862, 96035861, 96037859, 96039857, 96041855,
96042854, 96043853, 96044852, 96045851, 96047849, 96049847, 96051845, 96052844,
96053843, 96054842, 96055841, 96057839, 96059837, 96061835, 96062834, 96063833,
96064832, 96065831, 96067829, 96069827, 96071825, 96072824, 96073823, 96074822,
96075821, 96077819, 96079817, 96096096, 97021876, 97022875, 97023874, 97024873,
97025872, 97026871, 97031866, 97032865, 97033864, 97034863, 97035862, 97036861,
97041856, 97042855, 97043854, 97044853, 97045852, 97046851, 97051846, 97052845,
97053844, 97054843, 97055842, 97056841, 97061836, 97062835, 97063834, 97064833,
97065832, 97066831, 97071826, 97072825, 97073824, 97074823, 97075822, 97076821,
97097097, 98181011, 98182012, 98183013, 98184014, 98185015, 98186016, 98187017,
98189019, 98281012, 98282013, 98283014, 98284015, 98285016, 98286017, 98301181,
98301811, 98381013, 98382014, 98383015, 98384016, 98385017, 98387019, 98389021,
98401182, 98401281, 98401812, 98402811, 98481014, 98482015, 98483016, 98484017,
98486019, 98489022, 98501183, 98501282, 98501381, 98501813, 98502812, 98503811,
98581015, 98582016, 98583017, 98585019, 98587021, 98589023, 98601184, 98601283,
98601382, 98601481, 98601814, 98602813, 98603812, 98604811, 98681016, 98682017,
98684019, 98686021, 98687022, 98689024, 98701185, 98701284, 98701383, 98701482,
98701581, 98701815, 98702814, 98703813, 98704812, 98705811, 98781017, 98783019,
98785021, 98786022, 98787023, 98789025, 98901187, 98901286, 98901385, 98901484,
98901583, 98901682, 98901781, 98901817, 98902816, 98903815, 98904814, 98905813,
98906812, 98907811, 98981019, 98983021, 98984022, 98985023, 98986024, 98987025,
98989027, 99022877, 99023876, 99024875, 99025874, 99026873, 99027872, 99032867,
99033866, 99034865, 99035864, 99036863, 99037862, 99042857, 99043856, 99044855,
99045854, 99046853, 99047852, 99052847, 99053846, 99054845, 99055844, 99056843,
99057842, 99062837, 99063836, 99064835, 99065834, 99066833, 99067832, 99072827,
99073826, 99074825, 99075824, 99076823, 99077822, 99099099,
Thanks,
Hans, beautiful!
Best,
É.
(back
to main page)
(or try to solve this, which was sent on Feb. 10th,
2009 at 15:08 to Rec.Puzzles and never answered by anyone!)
(corrected version without typo)
Hello
Rec.Puzzlers,
Let's
pretend I was born the 29 of August 1951;
write this the usual administrative way [yyyymmdd]: 19510829
If
we substitute + to 5 and = to 8 we would have:
19+10=29
... which is arithmetically true.
Let's
note the above substitution [5+;8=]
To
be born the 29 of March 1971 would produce ->
-> 19710329
If
we substitue + to 7 and = to 3 we would have again:
19+10=29
The
substitution is now [7+;3=]
To be
born the 29 of January 1981 would produce 19810129
No
substitution can turn this into a sound equation.
For
instance [8+;1=] would give =9+=0=29
19810129
To
be born the 8 of December 1961 would produce 19611208
If
we apply [2+;6=] we would have ->
-> -> 19=11+08
... which we admit as being true (despite the leading zero of
08)
a)
What are all the "good" birthday dates with the substitution [a+;b=]
b)
Same question with [a-;b=]
c)
Same question with [a*;b=]
d)
Same question with [a/;b=]
(If
both birthday dates of you and your partner/lover/wife/boyfriend
etc. share the same substitution, please
let us know!)
;-)
Best,
Éric A. (eric tod angelini ta skynet
tod be) <- cleverly scrambled, uh!
__________
Last
minute:
Hans has just sent (Feb. 11,
2009) a “little bonus”: enjoy!
Number of 9-digit solutions:
=\+
0 1 2
3 4 5
6 7 8
1 -
2
- -
3
- - -
4
- - -
-
5
- - -
- -
6
- - -
- - -
7
49673 - -
- - -
-
8
50112 - -
- - -
- -
9 53219 -
- - -
- - -
-
Probable maximum (53219): see table here.