Assume that black starts with just the king on e8 and white has all her pieces in the normal opening positions. What is the shortest forced mate for white?
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1$\begingroup$ I've edited my answer to accomplish mate in 7 in all cases. It might be confusing, so let me know. $\endgroup$– CarlCommented Nov 10, 2015 at 19:22
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2 Answers
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Mate in Seven:
With some explanation to follow, this is mate in 3:
The king moving to row 8:
Kc8 -> Qe7 -> Kb8 -> Ba6 -> Ka8 -> Qb7
Kd8 -> Pd4 -> Kc8 -> Ba6 -> ( Kb8 -> Qb7 ) or ( Kd8 -> Bg5)
The king moving to row 6:
Kd6 -> Pd4 -> Kc6 -> Bf4 -> Kb6 -> Qc7
Kc6 -> Pd4 -> Kd6 -> Bf4 -> Kc6 -> Qc7
Kc6 -> Pd4 -> Kb6 -> Qd7 -> Ka5 -> Qc6
As such, any 4 moves that white can make to get black into that position or further down the move tree is mate in 7 at most.
The next position to explore is this creation after five moves. Is there any position the king can be that is not mate in 2? ( Red represents places the king can not be ).
Ka8: Qa5 -> Kb7 -> Qa6
Ka7: Qa5 -> Kb7 -> Qa6
Kb7: maybe
Kb6: Qh6 -> Ka7 or b7 -> Qa6
Kc8: maybe
Kc6: Qf7 -> Kb6 -> Qc7
Kd8: Qf7 -> Kc8 -> Qc7
Kd7: maybe
Ke7: Qd5 -> Kf8 or f6 -> Qf7
Kf8: Qf7
Kf6: Qf7
Kg7: Qf7 -> Qh8 -> Qg8
Therefore, if black should live beyond 7 moves, black needs to reach b7, c8, or d7 on the fifth move. White's stragety is to first develop the mate in 3 scenario and then the bishop attack. After Pe4 -> k? -> Qh5, black's second moves could be:
Except for that we know of our mate in 3 scenario, black's only options to avoid this are:
White's third move is Pd4. If black is on column E, F, or G, black's only hope to get to b7, c8, or d7 require moving to column D. However, white's 4th move will be Qf7 and this is the mate in 3.
Therefore, black's third moves are:
About our mate in 3 scenario: Things have become worse for black with the development of Pd4. Qf7 is now mate in 2, which means in can be white's fifth move.
Black can be on the right or the left of the board. If black is on the right, it can not reach b7, b8, or d7 by it's fifth move. This means that white can just develop the bishops.
If black is on the left hand side, the bishop development must be abandoned because it can not stop the king from becoming safe ( maybe ).
Instead, white's fourth move is Qf7. If black is on row 7, it must move to row 6 because row 8 is certainly mate in 3 at most. Black's fourth moves are as follows:
White now has three moves to clean up:
Kd4 -> Bf4 -> Kc4 -> Qc7
Kc4 -> Bf4 -> Kb4 -> Qc7
Kb6 -> Bf4 -> Ka5 -> Qa7 -> Kb4 -> Pc3
Ka5 -> Qa7 -> Ka5 -> Pc3
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$\begingroup$ Pawn movements aren't actually that bad, example: i.sstatic.net/7qefW.gif $\endgroup$– SleafarCommented Nov 10, 2015 at 18:52
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$\begingroup$ Intriguing! I am hoping someone brainier than me will check this :) $\endgroup$– SimdCommented Nov 11, 2015 at 19:51
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Here is a possible ...
... 8 move answer, which allows to ignore all variants of black King movements. No matter what black is trying, white can always make the shown moves.
Edit:
I managed to survive 7 moves against a computer, but there are too many variants to list them all here.
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$\begingroup$ @Lembik is that the answer? Do you know the answer? $\endgroup$– CarlCommented Nov 9, 2015 at 2:13
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1$\begingroup$ @Carl I suspect you can do it in 7 moves, but you will need a computer to check and list all variants. $\endgroup$– SleafarCommented Nov 9, 2015 at 5:22
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$\begingroup$ I'm quite certain the answer is seven, but yes, collecting them isn't easy. $\endgroup$– CarlCommented Nov 10, 2015 at 6:00