A friend told me about a chess game he had seen. At certain moment, the only pieces on board were a Queen at h8, a Rook at g6, and the Kings at h6 and g8. He didn't remember what color was each piece, but it can be worked out... how?

      +---+---+---+---+---+---+---+---+
      |   |   |   |   |   |   | K | Q | 8
      +---+---+---+---+---+---+---+---+
      |   |   |   |   |   |   |   |   | 7
      +---+---+---+---+---+---+---+---+
      |   |   |   |   |   |   | R | K | 6
      +---+---+---+---+---+---+---+---+
      |   |   |   |   |   |   |   |   | 5
      +---+---+---+---+---+---+---+---+
      |   |   |   |   |   |   |   |   | 4
      +---+---+---+---+---+---+---+---+
      |   |   |   |   |   |   |   |   | 3
      +---+---+---+---+---+---+---+---+
      |   |   |   |   |   |   |   |   | 2
      +---+---+---+---+---+---+---+---+
      |   |   |   |   |   |   |   |   | 1
      +---+---+---+---+---+---+---+---+
        a   b   c   d   e   f   g   h

If the Rook had been at g7, what would have been the colors?

First assumption:
One of the Kings was the last piece to move

Since a King can't move into check, the Queen and Rook must both match the color of the King which last moved.  Unfortunately, the other king is also attacked by both the queen and rook, and therefore this first assumption is wrong.


Second assumption:
The Rook moved from a different square to its current position.

The rook cannot have moved from a position that interposes between the Queen and either King.  Therefore the Queen was already attacking both kings, and this assumption is wrong.



Third assumption:
The Queen moved from a different square to its current position.

The queen would have had to move from a position that didn't already put both Kings in check (so not from G7 or H7).  But if it did not interpose between the rook and either King, then one of the two kings was already in check by the rook.  Therefore, this assumption is also wrong.


What's left?

Well... if there was a piece on H8 on the previous move, and a WHITE pawn on G7, then the last move could have been G7 x H8, promoting the pawn to a WHITE Queen.

This WHITE QUEEN is now putting one of the two kings in check.

Let's see what we can find out now:
Fourth assumption:
The G8 King is white.

Then the King on H6 is black.  Since the H6 king must not be in check, the G6 Rook is also black.  If this is true, then the white player could not have "queened" his pawn (it would have put his king in check).  Therefore, the fourth assumption is wrong too.

Therefore the G8 King is black, the H6 King is white, and because the white player made the last move (his pawn x H8), the Rook must also be white.

Epilogue:
All the pieces are white, except the black King on G8.  Who is now in check and faces two moves King to F7 or King x H8--both of which lead to a loss, so Black resigned.

Posted by Thalamus on 2004-08-04 12:15:46