I was saddened to hear of the recent death of Raymond Smullyan at the impressive age of 97. Smullyan was a mathematician, stage magician and concert pianist as well as a philosopher, but was best known as the author of many books on logic.
He was also interested in chess and published two books of ‘chess logic’ puzzles based on retro-analysis: The Chess Mysteries of Sherlock Holmes (1979) and The Chess Mysteries of the Arabian Knights (1981). My bookshelf includes the latter, but not, as far as I can recall, the former. In Smullyan’s puzzles the solver has to use logic to work out how the position was reached, rather than, as in most chess puzzles, what should happen next.
Here’s his best known puzzle.
Set up this position on your board: a white bishop on a4, a black bishop on d5, black rook on b5 and black king on d1.
In the Arabian Knights book Smullyan explains that Haroun Al Rashid, the White King, has made himself invisible, a trick he learnt from a Chinese sorcerer. He is on one of the 64 squares of the enchanted chess kingdom, but no one can see him. Your task is to discover his location.
You might like to work it out for yourself before reading on.
You’ll spot that the black king is in check from the white bishop, but that there is no possible last move for that piece. But if Haroun Al Rashid is on b3 he will be in what appears to be an illegal double check from the black rook and bishop.
You’ll need a bit of lateral thinking to realise that this double check is not quite impossible: it could come about from an en passant capture.
This is how the position might have arisen (the black bishop could be somewhere else on the long diagonal). Black plays 1… Bd5+ and the game continues 2. c4 bxc3 (en passant), giving double check from the rook and the bishop by opening two lines, and then 3. Kxc3, giving you the required position. So the answer is that Haroun Al Rashid is on the c3 square.
This was first published by Leonard Barden in what was then the Manchester Guardian in 1957, but, as Barden had been sent the puzzle without any further information, the composer was not named. A few weeks later, Smullyan made contact with Barden, who later published several more of his chess logic puzzles.
By way of a postscript to last week’s article, I have a more conventional puzzle for you to solve.
Black to play: choose your next move.
You might recall that last week I demonstrated how my two most recent games featured missed opportunities for very similar tactics: sacrificing a rook for a pawn to set up a fork regaining the rook.
Since then I’ve played another league game, and again I was awarded the white pieces. In this position my opponent has an extra pawn on c3 which might not be very safe, while I might also be thinking about taking advantage of the slightly insecure black king by playing Nxg5.
They say things come in threes, and, for the third consecutive game both players failed to notice the possibility of a very similar combination.
Black can play 1… Rd1+! 2. Rxd1 c2 winning material by forcing the white queen away from her protection of the rook on b5. White’s only hope now is to give up the exchange: 3. Rxb6 axb6 4. Qb3 cxd1Q 5. Qxd1. Instead, Black, who was starting to run short of time, played Rd6, and, a few moves later, panicked and gave up material unnecessarily. I eventually won the game.
This is slightly harder from last week’s positions. Firstly, it involves a sacrifice on a vacant square. Secondly, there’s the additional motif of deflecting the white queen so you have to see one move further ahead. The basic concept is quite similar, though, and again, if you look for checks, captures and threats, you should be able to find it.