Correcting the solution for the problem presented on pg 93, ‘The Case of the Dropped Pawn,’ from The Chess Mysteries of Sherlock Holmes by Raymond Smullyan
Holmes and Watson walk into the following game in progress where a white pawn had been knocked off of the board. Given that neither king had yet moved in the game, we must determine on which square the pawn stood.
This is an excellent puzzle, but unfortunately this board represents an impossible situation. However, if the Black bishop on f5 were instead on a6, the situation would no longer be impossible and Smullyan’s solution would be appropriate.
Alternatively, had the Black knight be in virtually any other square, then there would be a different solution (but the situation would still be possible).
Considering that the dropped pawn is supposed to be on the board, we see that all the original pawns are present and so no promotions have been made. White’s only capture must have been the Black rook on h3. But the only way the Black rook could get to h3 is Black’s pawn on b7 made a capture on b6. The only White pieces that have been captured are a rook and a bishop, but the captured (queen’s bishop) only moves on black squares. Therefore the b7 pawn captured a White rook. Since the kings haven’t move and the White king’s rook does not have a way to escape the 1st rank until the Black queen’s rook is captured on h3, it must be the White queen’s rook (which started the game on a1) that was captured. In order for it to escape, the pawn from b2 must have moved to b3 to let the queen’s bishop out, and the pawn from c2 must have moved to at least c4 – allowing the White queen’s rook to escape and be captured on c6, so that the Black queen’s rook could move out to be captured on h3. Following this, the White queen’s bishop at some point is captured on b6 and the White king’s rook moves to a1, which means that the dropped pawn must be on c4.
The problem is the Black bishop shown on f5. Since no promotions were made, it is an original bishop – the Black queen’s bishop – and it started the game on c8. Since it could not have escaped its home square until the White rook was captured on c6, and that rook couldn’t get to c6 until there were pawns on b3 and c4, the Black Queen’s bishop was never able to get to f5. Indeed, in this game, it would still be restricted to being on a6, b2, b4, or c8 (which is not), making the board we are presented in impossible situation. This error can is easily remedied by placing the bishop on one of the above mentioned squares.
Alternatively, if we put the Black knight shown on c5 on virtually any other square, we get a different solution, but still maintain a legally achieved board. The dropped pawn would then have resided on c5 (which allows the Black queen’s bishop to reach its location on f5), which is another way the problem can work.
