Deductive Puzzle #22

One of the White Knights has not moved in this game! Which is it?

This one looks hard -- it's clear, though, that the last move was Whites (it's actually Black to move) and that it was an en passant capture of a Black pawn on d5 for checkmate (likely from the e file, but I can't be certain that the pawn now on d6 didn't capture it's way over to c5).

[Edit: based on this we can also deduce that black's light squared bishop was also captured on its original square since the e-pawn was just on e7 prior to black's last move]

There seems to be a fundamental flaw with this puzzle -- here's why:

The knights can even interpose positions. For example:

I don't see how that is a flaw exactly. Its not that the position is impossible if it has moved, merely that its movement is not necessary to reach the position, while the other Knights movement is.

Yeah, fair enough actually -- one of the Knight's not having moved is in the premise so it doesn't need to be proved that it hasn't, just which one mustn't have.

A good starting point (I presume you mean d7 on the bishop thing). So the previous white move was exd6 e.p. (or cxd6 e.p.) and before that was ...d5 by black. But before that, what could white's move have possibly been? the only way for the position ot be legal is if a piece was blocking the bishop from a2. The only possibility for that would have been a pawn on c4 moving to c5. This means that there are 6 missing black pieces, and white's pawns had to make at least 5 captures. Furthermore, as you've pointed out, the c8 bishop was captured on c8, and therefore not by a pawn. So black's remaining missing pieces were all captured by white pawns. Something was captured on the g file. The d-pawn was taken en passant as discussed. Both knights and a rook were also taken. Furthermore, the a-pawn must have been taken somewhere. It must have come over at least to the c-file. So the a-pawn captured at least twice and the f-pawn captured at least twice. I feel like I'm getting close...

Hmm, looking closer at the last few moves, it occurs to me that black's last move -- d7-d5 blocked check from the Bishop, which poses exaxtly  the same problem as the line of thinking that proves the last move was en passant:  How did this position where the Bishop can't have moved to the square it's currently checking the king from without starting on another sqaure that also checks the king arise?

There is only one possible answer -- the move before d7-d5 had to have been a White pawn push from c4 to c5 (the pawn in question actually being White's e pawn)

This means that we've got all six black captures accounted for:

1. Black's e pawn on the previous move to deliver checkmate
2. Black's light squared Bishop on c8
3. A peice -- not a pawn -- on the g file by either White's f or h pawn (can't be sure which)
4. A peice, possibly Black's h pawn, but not necessarily on c3
5. Two more captures of pieces on d3 and c4 by White's e pawn

Our posts may have crossed, but we're on exactly the same wavelength WanderingWinder.

I was initially thinking the solution may lie in how and when White's dark squared Bishop escaped (if it all) and what bearing this has on the same questions for White's queen side Rook (if it escaped at all).

Upon a closer look at this though, White's missing a Rook, a Pawn and a Bishop and I see two captures by Black on g6 and h5 meaning there's only one remaining capture available for Black's a-pawn to get into the path of one of the remaining pawn captures (by your analysis WinderWinder), but these all happened on the c-file or further.

So how is this possible?  The a pawn must have made that last capture, promoted to another piece and then found it's way over to the c-file or beyond to be captured by a pawn.  But how did it promote if there are no remaining captures available?  It promoted on b1, and therefor it is the g1 Knight that has not yet moved in this game.

okay