Self-protecting
Chess (SPC)
Hello Chess Fans,
Self-protecting Chess diagrams are legal chess positions with 8 white pawns, 8 white men and no black piece
at all (but one empty
square, at least, must be available for a Black King: should
the Black King be added there, then the diagram would become
« fully » legal —
according to the normal chess
rules).
The SPC concept
claims two things:
1) every white piece protects exactly one other white piece
2) every white piece is protected by exactly one other white piece
This can be achieved
by one giant loop (like in diag.1a), where A protects only B, which protects
only C, which protects only D, ... until P which protects
only A (start with the Queen on
a1 and check the loop):
diag.1a
(one giant
loop)
If you put a Black King on a6 (diag. 1b), the position becomes « fully » legal (the diagram
hereunder could arise from a normal chess game; the d7 pawn, for example, could have been coming from h2, after having made 4 captures. Now that the concept of « legality » of a SPC position
is clear, no more Black
Kings will be shown):
diag.1b
(one giant
loop with Black King)
One could achieve the same task with
more than one loop; we show here (diag.2a and 2b) a 2-loop and a 3-loop
solution:
diag.2a diag.2b
(two loops) (three loops)
Is this old hat?
I’ve started to play with this
idea 15 years ago -- but lost ALL my notes & diagrams (which is
a shame, some of them were full of surprises).
Questions (among thousands
— I’ve forgotten some of the answers):
- create
a legal SPC diagram with 6 loops and one white pawn per column (a solution here)
- create
a legal SPC
diagram where the 16 white pieces fit in a 7x7 sub-square of
the board (is this
possible? I’m not sure...)
- leave
a pawn aside, then build a legal
SPC with the 15 remaining pieces, two of which only
are on dark squares (this puzzle is difficult, one solution is here; if you can add the last pawn to the diagram, I’ll offer you
64 US$!)
- etc.
This genre is great fun! If you find interesting things, please let me know [eric (dot) angelini (at) skynet (dot) be]: I’ll publish
them here!
And don’t forget to triple-check your diagrams: one forgets almost always a doubly-protected piece somewhere...
---
January 27th,
2008 note :
Bernd Schwarzkopf, from the Retro Mailing List, writes
that this is not new (at least 1961 !) :
(...) the
idea is old,
look:
Fred Galvin
Journal of Recreational
Mathematics
April
1961
wKd1, Qc1,
Rg8, Rh2, Bg3, Bh1, Sa7, Sb7, Pa5,a6,b5,b6,d5,e4,e6,f7
Each man protects exactly one other man; 3 loops.
(bK could
be on b3 or h5.)
Jexon J. Secker
The Problemist
May 1980
wKe1, Qa2,
Re8, Rg6, Bf1, Bg5, Sc1, Sc5, Pb2,b4,c3,d7,f3,f5,g2,g4
Each man protects exactly one other man; 1 loop.
Colin Vaughan
The Problemist
January 1983
wKg6, Qb7,
Rg8, Rh7, Be6, Be7, Sc7, Sd6 (no Pawns)
Each man protects exactly one other man; 1 loop on a 7 x 3-rectangular.
Clive Grimstone
The Problemist
January 1983
wKh6, Qe7,
Rf5, Rh8, Bd4, Bg6, Sd5, Se6 (no Pawns)
Each man protects exactly one other man; 1 loop on a 5 x 5-square, 23
squares unprotected
(maximum).
Colin Vaughan
Caissas Schloßbewohner
1983
wKg3, Qd5,
Ra7, Rb1, Bd4, Bh7, Sf1, Sf4 (no Pawns)
Each man protects exactly one other man; 1 loop, 4 squares unprotected
(minimum).
My article in Feenschach 71, November 1984, page
475-476: "Wer deckt wen?"
("Who protects whom?")
with reprints of some problems above
and:
Herbert Adamsky
& Bernd Schwarzkopf
feenschach 71
November 1984
wKg3, Qf1, Ra4, Rg8, Bc3, Be2, Sc7, Sd7, Pa2,b2,b3,b6,e6,g6,h2,h7
Each man protects exactly one other man; 6 loops.
(bK could be on e4.)
Herbert Adamsky
& Bernd Schwarzkopf
feenschach 71
November 1984
wKa5, Qc8, Rf3, Rh6, Bd5, Be5, Sb2, Sd1, Pb4,d4,d7,e2,e4,f1,g5,h4
Each man protects exactly one other man; 7 loops, but 1 Pawn on first rank.
(bK could be on a7 or h1.)
Best,
Bernd
... not new but still fun !
Thanks
Bernd !
Best,
É.
---
All diagrams were created
on-line here.
A similar challenge involving 32 units, there.
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