The Seven problem
I’ve
posted on the Retros mailing list, December 12th, 2009, this “problem without diagram” (please forgive my bad
English):
> Hello,
hope
this pb won’t be cooked seven times...
...
“For its 7th move,
Black has 7 different ways
to checkmate the
White King placed on e7 :
where are
the 7 remaining black pawns?”
Best,
E.
---
I
got almost immediately this reply from G. (spoiler inside -- please scroll):
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> Hi Eric -
You always come up
with interesting ideas! The stipulation
may be ambiguous: "the 7 remaining black pawns" could mean "the
7 black pawns that are left on the board" or it could mean "the seven
other (i.e., non-e7) pawns."
It seems that a
7-mate scheme is possible either with the e7 pawn moving to e6 and staying on
the board, or with the e7 pawn moving to e5 and getting captured. If the e7 pawn gets captured, the e2 pawn has
the option of playing to e3 or e4, allowing a bQ mate
in the former case and a second mate by the bP/bB
battery in the latter case. In any event, I think the solution is one of the
variants of the following:
1. d4 e6 2. Kd2 Bb4+ 3. Ke3 c5 4. Ke4 Nf6+ 5. Ke5 O-O 6. Kd6 Qc7+ 7. Ke7 etc.
Thanks for the
entertainment!
Best,
G.
---
The
perfect answer; here are the two possible (I’m still not 100% sure) end
diagrams, when you interpret my bad "the 7 remaining black pawns" as "the 7
black pawns that are left on the board".
In the first one the White pawn d2 has moved to
d4; in the second one only to d3. Both movements allow 7 mates later in the
game.
Case #1, White pawn on d4:
Case #2, White pawn on d3:
Best,
É.
____
Mario Richter
wrote to me the next day:
My computer says,
that under the assumption, that bPe7 has been captured during the game, there are 4 different positions after White’s 7th
move, which allow 7 different mates, the two you mention on the above webpage:
rnb2rk1/ppqpKppp/5n2/2p5/1b1P4/8/PPP1PPPP/RNBQ1BNR
rnb2rk1/ppqpKppp/5n2/2p5/1b6/3P4/PPP1PPPP/RNBQ1BNR
plus
two, where the wK left e1 via [e2 or] f2:
rnb2rk1/ppqpKppp/5n2/2p5/1b6/5P2/PPPPP1PP/RNBQ1BNR
rnb2rk1/ppqpKppp/5n2/2p5/1b6/4P3/PPPP1PPP/RNBQ1BNR
G. wrote:
> It seems that
a 7-mate scheme is possible either with the e7 pawn moving to e6 and staying on
the board.
Yes indeed - and a
little bit surprising: In this case the final position is even unique!
rnb2rk1/ppqpKppp/4pn2/2p5/1b1P4/8/PPP1PPPP/RNBQ1BNR
Best regards,
M.
Here
are the two positions Mario mentions
where the wK left e1 via e2 or f2 (same seven mates as just above in
red):
And
here is the position where no capture was made during the game:
We
could thus rephrase our initial request in a lighter mode:
Éric Angelini & Mario Richter
Retros Mailing List Dec.22nd, 2009
1+0
“Add
31 chess pieces in order to
allow Black, for its 7th move, to
have 7 different ways to checkmate
White”
Best
and thanks to G. and M.!
É.
__________
(back to main chess
page here)
(next “Five
Easy Pieces” pb there)