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Lots of pieces are tangled here.
Can you find mate in one?

enter image description here

Small hint to guide you in the right way:

If you look at this position as a normal chess puzzle, the answer might be easy. However, notice the retrograde-analysis tag. To fully solve the mystery in this position you will need to dig deeper!

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    $\begingroup$ @Evorlor I added an "executive summary" to the end of my answer. It's not quite on the "crystal clear to a layperson" level, but that's probably as non-chess-player-friendly as it's ever going to get, I'm afraid: this puzzle is really heavy on the required assumptions and analysis. $\endgroup$ – Bass Jun 27 at 7:42
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    $\begingroup$ @Evorlor you should probably take the time to learn chess ;-) $\endgroup$ – Emobe Jun 27 at 10:44
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    $\begingroup$ Could you add more context to this puzzle? Which side is black and which is white? I don't think it's clear from the board state (Though I'm a chess noob so maybe it's clear to others). Also whose turn is it? Is it part of the puzzle to find out which player can mate in 1? $\endgroup$ – popctrl Jun 27 at 15:13
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    $\begingroup$ @popctrl As for which side is which, I believe that when the rows are numbered, row 1 is always white's side, and row 8 is always black's side. $\endgroup$ – Admiral Jota Jun 27 at 19:16
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    $\begingroup$ Wow. This is a fantastic puzzle. So much depth in analysis and so nicely constructed and even adding a red herring. Brilliant. $\endgroup$ – Sid Jun 28 at 3:21
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Since the puzzle turned out to be way hairier than expected, my earlier answer got quite messy and hard to follow, so here's a complete rewrite. It's still very clunky, but I hope it's much clearer than the earlier one. Also, there's an executive summary at the end, if you are not interested in all the gory details.


First, we'll need to make some general observations. If they seem to be overly complex, try to hang on: every single one of these will turn out to be important. (Yes, really!)

Observation 1: White has 15 pieces on board, and black has a doubled pawn on the b-file, and a pawn on the c-file.

Consequence 1: The only white piece that was captured was taken by black's a-pawn. No other white pieces were taken.

Consequence 1.1: The five missing black pawns were either taken or promoted on the file they started on.

Observation 2: Assuming minimal captures, white's pawns are all identifiable, up to the pawns on d-file being interchangeable. The only missing white pawn is the h-pawn.

Consequence 2: The piece taken by black's a-pawn was white's promoted h-pawn. (Or another white piece, and the h-pawn was promoted to replace it. Since it doesn't matter in which order the capturing and the promoting happened, I'll just keep talking about "capturing promoted pawns" when I mean both of these possibilities.)

Observation 3: White's b-pawn has ended up on the d-file, and black's c-pawn is still on the board. Also, all black's non-pawn pieces are still on the board.

Consequence 3: White's b-pawn has taken a promoted black pawn on the c-file, and the black d-pawn on the d-file. (Either that, or two promoted black pawns. The former case is the relevant one though.)

Observation 4: White's g-pawn has taken black's f-pawn on f3.

Summary so far: Out of the 5 missing black pawns, we have accounted for 2 captured as pawns (on d and f files) and one captured promoted on the c-file.

Observation 5: In order to promote the h-pawn, white must have cleared the path somehow. There are three options:
1. white took black's h-pawn
2. white's h-pawn took black's g-pawn
3. white's h-pawn took another black piece on the g-file, and a pawn was promoted to replace it.

Consequence 5: no matter which of the three cases occurred, black lost one promoted/promotable pawn.

Observation 6: black's e-pawn was always blocked from promoting. The above cases have accounted for all the other black pieces, so it was impossible for white's d- and e-pawns to have swapped places by capturing, which could have opened the way for the e-pawn to promote.

Consequence 6: Either one or two black pawns were promoted. If two were promoted, one of them was captured on the g-file. In either case, one promoted pawn was captured by white's b-pawn on the c-file. In other words, all promoted black pawns have been captured by white pawns.


And now, FINALLY, we are ready to tackle the puzzle!

At first glance, it looks like

1. Nxc4#

could be the solution. Sure, why not. Let's check that the position could have been reached by legal play, though!

The black pieces are pretty much clumped up, so we can list all black's possible last moves:

  • Queen moved to c1 - impossible, because it would have started on a square where it was giving check
  • Pawn d2 promoted to Queen on c1 - impossible, because it would require a capture (see "consequence 1")
  • Knight took on b4 - impossible, requires capture.
  • Knight moved to empty b4 - seems plausible. But let's investigate further!

If black's last move was Nb4, then it follows that white's previous move must have been Bxc3+. If not, then the white bishop would have been giving check on white's turn, which is of course illegal. But this poses a problem: there cannot have been anything on c3 for the white bishop to capture, because above we have accounted for all promoted black pieces (see "consequence 6"), and the only pawn that could have reached that square is still on c4.

From all this, is follows that

It cannot be white's turn!


Well, where is the mate then?

Given the information from above, we can try to figure out white's last move. It must be something that enables a new previous move for black, since if it doesn't, we know from above that black has no moves.

Let's explore the four possibilities for this case:

Possibility 1: White's last move was Nb6. This enables a pawn move for black's previous move, but then the white move before that is impossible; there's no way the white rook can be giving check:

  • the rook cannot have moved to c5 to give check
  • the white pawn on a6 cannot have been on b5, discovering the check, because it would require a capture, and all black pieces are accounted for. (Black's only "unaccounted for" piece is the e-pawn, which cannot have left the e-file.)
  • and obviously, white's queen couldn't have revealed the check either.

Possibility 2: White moved something that enabled the black queen to move last

  • sadly, no such moves exist.

Possibility 3: White took black's e-pawn, which was black's previous piece to move

  • Since black's e-pawn cannot possibly have left the e-file (see conclusion 1), the only square where this capture could have happened is e3, and the capturer could only have been white's d-pawn. That would mean that one of the white pawns on the d-file is actually white's e-pawn. That could only happen if one more black piece was captured, which we already know didn't happen, so this line is also impossible.

Possibility 4: White moved something that enabled the black knight to move last

This looks promising, but there's still the problem of finding a suitable move.

  • It could not have been a bishop move, because the bishop would still have been on the black king's diagonal
  • It could not have been pawn d3 to d4, because now the knight has no square from which to jump into its current position
  • So it must be pawn d2 to d4.

This enables a move for the black knight, because it opens up a new previous move for white: now the bishop can have come from somewhere that's not on the black king's diagonal.

In other words, three half-moves ago, the board must have looked like this:

enter image description here
(white's dark square bishop could also be elsewhere on the long diagonal)

From there, the only way to reach the current position is

1. Bc3+ - Nb4
2. d4

Which finally allows for the long sought after mate in one:

2. - cxd3 e.p.#!

Phew! What a ride!


TL;DR:

At the first glance, it looks like 1. Nxc4#might be the answer. However, a very complicated analysis proves that it cannot be white's turn to play. Starting again with the assumption that it's blacks turn, another round of analysis proves that white's last move can only have been "pawn from d2 to d4". This enables black's c-pawn to capture en passant, which checkmates the white king.


I may have missed some specific variations, so please drop a comment if you notice one. And thanks again, OP, for another brilliant puzzle!

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    $\begingroup$ I figured that it would be something like this-I just couldn't quite figure it out myself. $\endgroup$ – Rewan Demontay Jun 26 at 22:19
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    $\begingroup$ @Bass You're getting pretty good at this :) I think you covered everything, will double check later. $\endgroup$ – shoopi Jun 27 at 4:17
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    $\begingroup$ @tgm1024 retrograde chess and making moves backwards truely can be a little confusing. Sometimes it helps trying to recreate the game and seeing the problems in the position first hand. The line you suggest is not possible - if the knight moves black is in check by the bishop which has to be accounted for. Also, white can't play d2-d4 while the knight is on d3. $\endgroup$ – shoopi Jun 27 at 20:34
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    $\begingroup$ The funny thing is I saw the en passant before the Nx move. $\endgroup$ – MooseBoys Jun 28 at 7:36
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    $\begingroup$ @racraman rook takes c2 isn't checkmate, white can block with the bishop. $\endgroup$ – Bass Jun 28 at 11:25
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To add on to Glorfindel's answer,

...cxd3 is also mate, assuming white just played d2 to d4. The question doesn't state if we're finding mate for white or black.

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    $\begingroup$ Nice spot there! $\endgroup$ – Rewan Demontay Jun 26 at 21:08
  • $\begingroup$ +1 As this observation is very important here, as seen in the top answer! $\endgroup$ – yo' Jun 27 at 19:47
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    $\begingroup$ It was proven already that it cannot be white's turn though. There is only one mate. $\endgroup$ – tgm1024 Jun 27 at 20:11
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Nxc4

is mate because

pawn b5 is pinned

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    $\begingroup$ Beat me by about ten seconds... $\endgroup$ – Jeff Zeitlin Jun 26 at 19:24
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    $\begingroup$ I'm pretty sure that's not right. :-) $\endgroup$ – Bass Jun 26 at 20:50
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    $\begingroup$ This isn't the right answer. It can be proven that it isn't white's turn. See other answers. $\endgroup$ – tgm1024 Jun 27 at 20:11
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    $\begingroup$ True - analysis rules out this possibility, but this answer still has value in showing the first try, which is somewhat of a red herring after all. $\endgroup$ – shoopi Jun 27 at 20:19
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    $\begingroup$ @tgm1024: No, it cannot. Many chess puzzles exist that spawn from unreachable positions; therefore "the position is reachable from the starting board" is an invalid assumption. $\endgroup$ – Joshua Jun 28 at 1:21
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cd e.p.

Explanation

1.

It is black's turn to move. The only black piece for which there are free fields it could have moved from in the previous half move is the Queen. However, on all candidate origins the queen would have been checking the white King. In such a position, white must move (its King out of check) or loses by checkmate.

2.

No mate opportunities for black under null move heuristics. Assuming that black had moved in the last half move, the legal moves that would put white into check are: - capture c2 with either Queen or Rook. This can be countered by Bd2. - Move the Queen to d2 or d-f1. The white Rook or King would capture in turn

3.

Conclusion: the preceding half move of white must have created a move opportunity not available under null move heuristics. That can only be a pawn move allowing for capture an passant. The only white pawn on rank 4 is on file d.

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    $\begingroup$ On spoiler block 1: there are more possibilities to rule out than that; for example, black's knight could have taken a promoted white rook on b4. (There are a couple of other possibilities too.) On spoiler blocks 2 and 3: in retrograde problems, you can only start with an en passant capture after you have proven the double pawn move without using the assumption that a solution exists. $\endgroup$ – Bass Jun 29 at 3:23

protected by Bass Jun 28 at 4:15

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