A tribute to Raymond Smullyan (1919-2017)

The logician and mathematician Raymond Smullyan passed away in February this year, at the age of 97. An astonishing polymath, he gained a PhD in mathematics and was additionally a philosopher, pianist, and magician. He was also an expert on Eastern mysticism, and I briefly discussed his spiritual philosophy in an earlier Walkabout column (12 Dec. 2012). To the general public, he was perhaps best known for his books of logical puzzles, the first of which was titled, What is the Name of this Book? But chess enthusiasts will remember him most for two collections of retro-analytical problems, The Chess Mysteries of Sherlock Holmes (1979) and The Chess Mysteries of the Arabian Knights (1981).

The Chess Mysteries must be among the most popular books on chess problems ever published. Smullyan wrote in an appealing style and the problems are accompanied by engaging storylines. The retros themselves – in which the tasks involve working out certain facts about the past of a diagram position – are proficiently devised, with a range of difficulty levels. Naturally the two volumes are fine introductions to the genre, and indeed Sherlock Holmes inspired me to create my first retros more than thirty years ago.

Here are two illustrations of Smullyan’s works. The first is quite straightforward, or “elementary” as Sherlock Holmes would say. Given it’s Black to move in the diagram position, is it legal for that player to castle? To answer this, we try to determine what occurred in the last few moves. White made the last move and it was Pa3, and just before that Black must have made a capture, because otherwise White would have no free unit with which to make a further retraction. The captured piece was one of the knights, since the only other missing white units are the rooks which couldn’t have escaped from the first rank. This white knight wasn’t captured by any of the pawns (none of which has a legal diagonal retraction), so it was captured by one of the four black pieces on the top rank. The a8-rook couldn’t have made this capture, however, because the uncaptured white knight on a8 would have no possible prior move. Likewise, if it were the c8-bishop which had captured the knight, then the latter on c8 could only have just come from the empty square d6, but such a retraction would be impossible because it implies that Black was in check by the knight on d6 while it was White’s turn to play. Therefore only the black king or the h8-rook could have captured the knight, which had come from d6 (to e8) or g6/f7 (to h8). That proves Black had previously moved the king or the h8-rook in the game, and now cannot castle.

The second problem is more complex but still not exceedingly difficult. Which of the three white rooks is promoted? Solving this requires dealing with a couple of preliminary questions. The first is: on which square did White’s missing e-pawn promote to a rook? Black has three missing pieces (rook, bishop, and knight) that were available for the e-pawn to capture on its way to the eighth rank. A rook promotion on the queen-side or the middle files wasn’t possible, however, because we are given the condition that neither king has moved, and such a promoted rook could not have left the top rank without dislodging the black king from e8 (e.g. by checking from d8). That means the e-pawn could only have promoted on h8 and the rook escaped via h6. The second preliminary question is: how did the d7-rook reach its current position? I shall leave the reader to answer that and solve the remainder of the problem!

‘Philosophy Looks At Chess’ and Raymond Smullyan

12 Dec. 2012