This position was reached in a normal chess game:

                   BLACK
     +---+---+---+---+---+---+---+---+
     | B |///| K |/R/| N |///|   |///|  
     +---+---+---+---+---+---+---+---+
     |/P/| P |///|   |///|   |///|   |  
     +---+---+---+---+---+---+---+---+
     |   |///| Q |/K/|   |/R/|   |///|   
     +---+---+---+---+---+---+---+---+
     |///|   |///|   |///|   |///|   |
     +---+---+---+---+---+---+---+---+
     |   |///|   |///|   |///|   |///|
     +---+---+---+---+---+---+---+---+
     |///|   |///|   |///|   |///|   |
     +---+---+---+---+---+---+---+---+
     |   |///|   |///|   |///|   |///|
     +---+---+---+---+---+---+---+---+
     |///|   |///|   |///|   |///|   |
     +---+---+---+---+---+---+---+---+
                   WHITE

a) Identify the color of each piece.
b) What was the last move?

Both Eric and Ken Haley are correct in the analysis they have given (see previous comments); however, the solution given to part b by Ken seems incomplete, as the rank of the black piece captured by the promoting white pawn has not been determined.

Obviously, as the capture occured as the white pawn promoted, the captured piece could not have been a black pawn.  It had to be either a queen, rook, bishop, or knight.  The only way to determine which piece it must have been is to consider the question: 'What was black's last move prior to the capture by the white pawn (now rook) on d8?'

So, let's back up one move.  It helps to pull out a chessboard and set up the position for yourself.  (It has been shown in prior comments that all pieces on the board are white, with the exception of the King on c8 and the pawn on b7 which are black.)  Now, replace the white rook on d8 with a white pawn on c7, and place a coin on d8 to represent the unknown black piece.  At this position of the game, it is white's move, and black has just moved.  So, what did black move?  Obviously not the pawn on b7, which has never moved.  He also could not have just moved his King, as the only available squares to have moved from are b8 (which would involve an imaginary check from 2 white pawns) or d7 (which involves an imaginary check from the white King).  Again to the reader - it will aid you to set the position up with a chessboard if you don't follow my argument.

So, the only black piece which could have just moved is the unknown piece sitting on d8.  What could it be?  If it was a queen, rook, or bishop, any square that it had just moved from would have involved it checking the white King, which could not be possible.  The only situation that seems to work here is that the black piece is a knight, and it has just been moved from e6 to d8.

Hence, the last move was a white pawn on c7 capturing a black knight on d8, and in doing so, promoting to a rook.  The move prior to that was the black knight moving from e6 to d8 - although it is unclear whether or not it captured a white piece there.

For those readers who find this problem interesting, you should read the wonderful books by Raymond Smullyan containing problems of this sort.  (I believe they are called "The Chess Mysteries of Sherlock Holmes" and "The Chess Mysteries of the Arabian Knights")

Thanks to pcbouhid for a good puzzle!

-John Reid

Posted by John Reid on 2006-01-12 18:52:11