Chess mysteries

Some of the best puzzles I’ve ever seen are the Chess Mysteries, created by Raymond Smullyan. They have given me hours and hours of intellectual stimulation.

Here is a typical example from his book ‘Chess Mysteries of Sherlock Holmes’. Consider the following chessboard. Black is in check-mate from White. Which side (north or south) is white, and which side is white?

 

The first observation is that this is very different from the normal kind of chess puzzle, which is of the type ‘White to mate in 3 moves’ or similar.

So how would you go about solving the seemingly intractable problem of which side is White?

The only clues you have are the ones from the chess board. Obviously, since black is in checkmate, the last move must have been white’s. So what was white’s last move?

Since Black is in check from the White bishop, either the bishop must have moved to administer check, or some other piece must have moved out of the way to discover check from the bishop. Consider the former case.

If the Bishop moved to administer check, where could it have moved from? Obviously only along the main diagonal. But on any square on that diagonal, it would already have been administering check to the king! That would invalidate Black’s previous move, and therefore it is not a valid possibility.

That leaves only the option that something moved out of the way to administer check. What could it have been? Not the queen, because it could have only moved away from b7 to discover check by the bishop, but at b7, the queen would already have been checking the black king. Not the White bishop on c5, obviously – it is on a black square. So it must have been one of the pawns. Either the pawn on d4 moved there from d5, or the pawn on e5 moved there from e4, or the pawn on h3 moved there from g2 (capturing a black piece). In the first of these cases, White is North; in the second and third, White is South. So which of these is it?

We can eliminate the last option straightaway. If there was a pawn on g2 until one move back, how could the white bishop have gotten to h1 in the first place? So no – that option is verboten.

In order to resolve the question of which pawn moved (of e4 and d5), it is necessary to cast your mind one step further back. Assume that the pawn (whichever it was) was moved out of the way to discover check by the bishop. What could Black’s previous move have been? If it was with the King, where could the King have moved from? It could not have moved into a8 (where it currently is) from a7, because at a7 it was in check from both the queen and the bishop on c5, and there is no prior move by white which could have discovered both checks at the same time. Of course it could not have moved from b7, due to the White King’s presence on c3.

So Black’s King could not have moved to a8 from anywhere! It seems an impossible position and a fruitless quest…

But there is another possibility. Could black’s last move have been, not with the King, but instead with another piece? What other piece, I hear you ask. There’s nothing else on the board! Well, it’s true that there’s no other piece on the board now, but there may have been a piece when Black made the last move. That piece was captured by the Bishop to deliver check.

This doesn’t seem to be any more promising, because where did the Bishop come from to capture this piece X?

Then (if you are the kind of person who solves this kind of problem) you will have an epiphany. Perhaps, before the bishop captured the piece X, it wasn’t a bishop at all!

How is that possible? It’s possible if the Bishop was a pawn that got promoted. And since it captured X on promotion, it must have promoted on h1. So white’s last move was bxa8=B.

And Black’s move before that was Xa8. (X could have been a rook or a queen or a knight).

And if white was moving down the board to promote, then obviously, white was playing North.

Nice, no? Here’s a link to Smullyan’s book, if you are interested in this kind of problems: http://www.amazon.com/dp/0486482014. He also came up with a sequel called Chess Mysteries of the Arabian Knights. Both are fantastic.

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