By the way, this came from Raymond Smullyan's The Chess Mysteries of Sherlock Holmes. It's full of great retrograde analysis problems. I'd recommend that book to any chess enthusiast.
1) Seeing as black king is in check, it cannot be Black Queen or Rook.
2) Last move was cxd8+ with promotion to rook. It's the only way the last move could have happened.
3) I suspect it isn't a White Pawn or a Black Knight, but cannot fully disprove those yet. 2 pawn captures could make it a white pawn, and one of the knights might be an underpromoted pawn (like the rook).
If you want to get the correct board each time, go to New Game, click on Advanced Options, click on the box that says play from set piece, set up the position, highlight the fen so that you can copy it, and paste it where it says Insert board form FEN.
The next thing you should determine is exactly what black piece did the white pawn just capture? As for your third point, there are seven white pawns currently on the board, and you just said that the eighth one promoted.
Apart from the doubled ones all the black pawns are on their original files, unless the d-pawn and trailing c-pawn swapped files by taking. The leading black c-pawn must have started life out as the f-pawn. To get there it must have taken three times and the leading a-pawn (starting from b7) took once. Each thing they took has to have been a piece (since white has 7 pawns and one just promoted) so black's pawns have taken exactly four white pieces. White is missing a total of 6 pieces, of which 4 have been taken on light squares. Two could have been taken on dark squares - or one on one of each colour if and only if the c and d pawns swapped round. If this has happenned (black takes with the c and d pawns so they swap files) then the missing piece cannot be a white one and the h-pawn cannot have promoted.
To get where it did to promote the white pawn had to take at least 4 black pieces. There are two places it could have started from c2: when it has to take 3 times to get to c7 and once to promote, or from b2 when it has to take a total of 5 times. For the b and c pawns to swap files we would need white to take a total of 6 pieces which is only possible if black hasn't promoted or has and the promoted piece has been taken (one of the pieces taken in this scenario is the a - pawn now on the b-file so it would need to have taken a white piece). Assuming this then the pawn started on c2. The piece just taken cannot have been a rook or a queen as there is no piece that could have moved to uncover a check on the white king and it couldn't have got there without going from a square where white was in check. Therefore the piece taken was the dark squared black bishop. Conceivably black could have promoted the h-pawn to a dark squared bishop. Since we know that the piece that fell off cannot have been a black rook or queen and the light squared black bishop can't be on h4 the only black piece it can be is the a-pawn - provided that black can't have promoted.
If the c and d pawns both took white pieces - then it can't be a white piece - black cannot have promoted (there's not enough pieces to take) so since it's not a major piece, a knight or the light squared bishop the piece that fell off must be the h pawn.
So it remains to be shown either that the c and d pawns have swapped round - or that black hasn't promoted (black can't have - otherwise the problem is impossible).
I'll give another hint in response to the last answer.
Therefore the piece taken was the dark squared black bishop.
That statement is not necessarily true. You say that the dark squared black bishop was able to get to d8. Look at e7 and g7, and you'll have to rethink that.
Conceivably black could have promoted the h-pawn to a dark squared bishop
If you still hold that a dark squared bishop was captured, then indeed Black must have done just that. By the same reasoning, then, there's no reason that the captured piece could not have been a knight.
Originally posted by Jirakon Whoa, that's doesn't look right.
[fen]2nR3K/pk1Rp1p1/p2p4/P1p5/1Pp5/2PP2P1/4P2P/n7[/fen]
White must have just played c7xN(B)d8=R+. This leads to two dark-square Bishops or three Knights for Black; he must have promoted. Pf7 is on c4, so Ph7 promoted via hxg2. Black made 5 pawn captures all on light squares; White's 6th missing piece, the dark-square Bc1, was not captured by pawns.
To promote, White had to make at least 4 P captures, not counting Bf8 who died w/o moving. This leaves one missing Black piece unaccounted for.
The piece on h4 can't be a bQ or bR (impossible check to both K's), nor a Bh4 (requires a 2nd Black promotion - impossible). The only piece left is a wB.
Originally posted by SwissGambit White must have just played c7xN(B)d8=R+. This leads to two dark-square Bishops or three Knights for Black; he must have promoted. Pf7 is on c4, so Ph7 promoted via hxg2. Black made 5 pawn captures [b]all on light squares; White's 6th missing piece, the dark-square Bc1, was not captured by pawns.
To promote, White had to make at least 4 P captures h K's), nor a Bh4 (requires a 2nd Black promotion - impossible). The only piece left is a wB.[/b]
Apart from one possible loophole, I agree with your answer - the only candidate is the dark squared white bishop.
We have to be certain that the h7 pawn went h7 ---> h3 and then took a piece on g2. Had the pawn that just promoted on d8 come from g2 then black's h - pawn could have taken a white piece on a dark square and still promoted. For this to be possible white would have to take with the pawn on f3, e4, d5 and c6 and finally on d8. That's 5 captures with the pawn, and the f7 bishop never moved for a total of 6 captures. For this to happen we need the f pawn has to take something on g3 to restore the final position and we've run out of things for it to take. So the pawn that became a rook started out on f2 and black must have taken on g2 - so your answer is correct.
Originally posted by DeepThought Apart from one possible loophole, I agree with your answer - the only candidate is the dark squared white bishop.
We have to be certain that the h7 pawn went h7 ---> h3 and then took a piece on g2. Had the pawn that just promoted on d8 come from g2 then black's h - pawn could have taken a white piece on a dark square and still promoted. For this to ...[text shortened]... t have taken on g2 - so your answer is correct.
Jirakon: That was a good puzzle - thanks.
Yep. Black's ...hxg3 requires two extra wP captures, and we only have one to spare.
A piece fell off of h4. What is it?
30 Apr '07 23:43
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