What is the quickest way to get a checkmate under the following conditions:
- The winning side moves the king on every move
- The starting position is Chess960?
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1Neither player can move the King in any Chess960 starting position, so this is impossible.– AllureCommented Aug 27 at 3:56
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2In some positions, you can castle on move 1 in chess960.– LucenapositionCommented Aug 27 at 6:07
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1@Lucenaposition: True. This means especially only Black can do this: 1.wpawn 1...castles 2.longcat x bpawn 2...K x longcat. This reduces the number of 960 positions severely. I find that very interesting and give it a quick try, if I get bored, I sic MatPlus on it :-)– Hauke ReddmannCommented Aug 27 at 7:44
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EDIT: 8 moves suffice! This surely can be shaved, why I don't post it yet.– Hauke ReddmannCommented Aug 27 at 7:53
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2 Answers
Pending a genius stroke from MatPlus, this might be the fastest way:
[FEN "bbrnnkrq/pppppppp/8/8/8/8/PPPPPPPP/BBRNNKRQ w - - 0 1"]
1. c4 O-O 2. Bxh7+ Kxh7 3. g3 Kg6 4. Kg2 Kh6 5. Kh3 Kh5 6. Rg2 Kg5#
(@mods: can 960 be made playable - i.e. KQkq works in 960 FEN? If so, please edit and delete this comment)
answered Aug 27 at 8:24
This problem can be solved computationally using the powerful "constraints" feature of Francois Labelle's Jacobi engine: https://wismuth.com/jacobi/latest/solver.html
> option FirstToMove white
> stipulation h#6
> condition Chess960
> constraint Xa8(0..0) Xb8(0..0) Xc8(0..0) Xd8(0..0) Xe8(0..0) Xg8(0..0) Xh8(0..0) Pa7(0..0) Pb7(0..0) Pc7(0..0) Pd7(0..0) Pe7(0..0) Pf7(0..0) Pg7(0..0) Ph7(0..0)
> constraint Xf8!g8~
A few comments:
- option "first to move white" implies also that black will deliver the mate. I.e. it's the equivalent of "halfduplex" option in Popeye.
- Jacobi handles variable officer positions using "X" to specify unknown unit. Castling counts as a king move, so 15 black units are prevented from moving by specifying their minimum & maximum number of moves as zero.
- We also say that the first move of the 16th unit is castling "!", followed by any number of other moves, "~".
- There are 360 solutions, all beginning "1.c3/c4 O-O 2.Bxh7+ Kxh7".
- 80% of the solutions follow the pattern given by Hauke, however there is an alternative approach where White also castles: (BBSSRKRQ) 1.c3 O-O 2.Bxh7+ Kxh7 3.O-O Kg6 4.h4 Kh5 5.Kh2 Kxh4 6.Rg1 Kg4#
- There are 9 different game arrays that work, 2 first moves, and 2 final blocking moves by wQ/R. There are then various other duals which lead to 8+2=10. 9x2x2x10=360.
- There are no solutions in 6.0 moves with queenside castling.
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1Now that's solving in style :-) Too bad for the immanent 1.c3/c4 dual, or one could make a "real" problem out of it. Point 6 doesn't surprise me, running to the border then takes too long, and a discovered check on an "epauletted" king (my 1st attempt) takes around 8 moves. Commented Aug 28 at 7:56