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I was recently introduced to this lovely mate in 1 puzzle. It’s best when shown on a physical chess board. But what is the smallest number of moves it would take to reach this position?

enter image description here

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    $\begingroup$ Very cool puzzle! $\endgroup$ Commented May 27, 2023 at 11:08

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The answer (EDIT: to the question as it was originally posted) is

Yes, the position is reachable.

The solution to the mate-in-one depends on

there being no indication as to which way the pawns are moving,

but in either case, there's nothing to stop a white piece, (say, a knight) from capturing all the other black pieces, and after that, it's very easy to arrange the pieces like shown.


EDIT: The new, edited-in question asks how many moves does it take to reach this position. As long as we assume the mate in one is solvable, we know the board orientation, and can calculate a lower bound for the answer by adding up the minimum number of moves it would take for each piece to reach its target square from its starting square, if it were moving alone on an otherwise empty board.

Doing so, we get that it's always going to take at least

7 (king) + 2 (queen) + 2 (rooks) + 8 (knights) + 4 (bishops) + 32 (pawns) =
55 moves

to reach this position.

Note that we won't bother counting the moves by the other player, since their only requirement is to put their two pieces to their places and wait,

while providing fodder for the pawn captures that enable the optimal movement of the queen and the rooks.

Now then, having established a hard minimum, we only need to prove that a legal game exists that reaches the given position with this minimal number of moves.

Here's a (very messy) example of such a game: (view on Lichess)

1. d4 c5 2. e4 c4 3. a4 c3 4. Nxc3 a6 5. Bxa6 b5 6. axb5 h6 7. Bxh6 e5 8. dxe5 d5 9. Nxd5 f6 10. Nxf6+ Ke7 11. Qxd8+ Ke6 12. Nxg8 Bd6 13. exd6 Ke5 14. h4 g5 15. hxg5 Kd4 16. c4 Nd7 17. Bf8 Rh7 18. g6 Rg7 19. Rh8 Rh7 20. gxh7 Ne5 21. f4 Nf3+ 22. Kf2 Bd7 23. Bc8 Bc6 24. b4 Kc3 25. Rxa8 Bb7 26. Kg3 Ba6 27. bxa6 Kd2 28. a7 Kd1 29. b5 Kd2 30. b6 Kd1 31. c5 Kd2 32. c6 Kd1 33. c7 Kd2 34. b7 Kd1 35. Ne2 Kd2 36. Nd4 Kd1 37. Nc6 Kd2 38. Nb8 Kd1 39. Kg4 Kd2 40. Kf5 Kd1 41. Kf6 Kd2 42. Ke7 Kd1 43. Qe8 Kd2 44. Kd8 Kd1 45. g4 Kd2 46. g5 Kd1 47. g6 Ng5 48. f5 Kd2 49. e5 Kd1 50. e6 Kd2 51. d7 Kd1 52. e7 Kd2 53. f6 Ke2 54. f7 Kd1 55. g7 Ne6#

So the final answer is

55 moves.

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    $\begingroup$ @simd added a sample game to show how that can be done. $\endgroup$
    – Bass
    Commented May 22, 2023 at 6:01
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    $\begingroup$ I've seen similar puzzles which would have the king and queen swapped (this puzzle would need the knight moved also) so one can prove that white is moving up the board. $\endgroup$ Commented May 22, 2023 at 11:07
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    $\begingroup$ @ralphmerridew Indeed. That situation would actually be reachable one move faster, because the second queen move wouldn't be needed. $\endgroup$
    – Bass
    Commented May 22, 2023 at 12:17
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    $\begingroup$ I love the number of questionable and blunder moves Lichess reports when you scroll through that... $\endgroup$ Commented May 22, 2023 at 13:42
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    $\begingroup$ @DarrelHoffman I love that it tells me how many moves white could mate in for a lot of the moves that lead up to the mate by black. $\endgroup$
    – Simd
    Commented May 23, 2023 at 10:55

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