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ThudnBlunder
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 Piece Wrong Colour (Chess)   Puzzle777.jpg « on: Dec 16th, 2010, 10:52am » Quote Modify

One of the pieces (not pawns) in the position below (from a legal chess game) is the wrong colour. Deduce which piece it must be.

 « Last Edit: Dec 17th, 2010, 11:39am by ThudnBlunder » IP Logged

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Obob
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 Re: Piece Wrong Colour (Chess)   « Reply #1 on: Dec 16th, 2010, 7:39pm » Quote Modify

What do you mean?  I was able to recreate the given board state legally.
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ThudnBlunder
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 Re: Piece Wrong Colour (Chess)   « Reply #2 on: Dec 16th, 2010, 7:53pm » Quote Modify

on Dec 16th, 2010, 7:39pm, Obob wrote:
 What do you mean?  I was able to recreate the given board state legally.

If it is given that one piece is the wrong colour, it is possible to deduce which one.
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aicoped
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 Re: Piece Wrong Colour (Chess)   « Reply #3 on: Dec 16th, 2010, 10:00pm » Quote Modify

i can reach a legal position assuming the white queen is actually a promoted pawn. I need 3 pawn captures to do this. so the king would have moved out of the way letitng the queen out for 1 captur
the knight would have been the second capture and the king side rook moving to g1 would allow black to queen. so black could have an extra piece  but since the "white queen" is still on the board, it isnt really a white queen but a black on. blacks last move had to have been Bh4 assuming this is correct.
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ThudnBlunder
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 Re: Piece Wrong Colour (Chess)   « Reply #4 on: Dec 17th, 2010, 2:05am » Quote Modify

on Dec 16th, 2010, 10:00pm, aicoped wrote:
 the knight would have been the second capture and the king side rook moving to g1 would allow black to queen.

Nice try, but the Black pawn on c7 requires four captures to get to g1.

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rmsgrey
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 Re: Piece Wrong Colour (Chess)   « Reply #5 on: Dec 17th, 2010, 6:32am » Quote Modify

Given that the pawns are all genuine, and assuming no promotions have taken place, the white rooks and bishops cannot have moved from the first rank (and the black bishops can't have reached it), and both queens are still in play, so the only pieces that could be the wrong colour are the knights - black still has both knights, so one of the black knights must be wrong. However, that would leave both kings in check, which is impossible.

Therefore, a pawn must have been promoted. The only missing pawn is the black c-pawn, which can only have been promoted by passing through f2, requiring at least three captures. With the white bishop at f1, only the missing white knight, one of the two missing white rooks, and one of the remaining white knight and white queen can have been taken by the pawn (which replaces the queen or second knight) - three captures, but a fourth is needed to promote at e1 or g1 since f1 is taken. Again a contradiction.

Therefore, the white bishop cannot have been at f1 the whole game. Since, given the continued presence of white pawns at e2 and g2 (assured from the problem statement), the only way the bishop could have left the square is by being captured, and the only way a bishop could have reached the square is by being promoted there, the bishop at f1 must be black. With the white bishops out of the way, the remaining missing white pieces (two rooks and a knight) can all be captured by black's c-pawn to allow it to reach the f-file.

I'll leave completing the proof that the position (with a black bishop at f1) can be reached legally to someone else.
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