How did that happen? December 28, 2001

"Retrograde analysis" sounds daunting, but is it a very enjoyable form of recreational chess, requiring humour and lateral thinking.

One of the great masters of the retrograde problem was T. R. Dawson, but the genre was brought to mainstream attention in a series of books by Raymond Smullyan entitled "Chess mysteries of Sherlock Holmes". They appeared in Hutchinson around 1980.

Smullyan's chess puzzle books are written in the style of the Conan Dolye tales. The presents problems that require the same kind of logic the master detective employed to track down his criminal adversaries. Typically Holmes and Watson will find an interrupte game Raymond Smullyan is a well-known mathematician and logician in New York. The introductory puzzle, shown on the cover of the book, is given below.

I had a memorable evening alone with Holmes, during which I learned more about retro-analysis than perhaps on any other occasion. "Here, let me set up a little exercise to illustrate the more normal type of situation," he said.

What was Black's last move?

“I call this an ‘exercise', Watson, since it is really too simple to dignify by the word ‘problem'. As you see neither side is mated – nor even in check. The question now is this: Given that Black moved last, what was his last move, and White’s last move?”

I thought for a while, then said, “Holmes, I’m sorry to be such a slow pupil, but the situation again seems impossible! Obviously Black just moved out of check from a7, but I don’t see how White could possibly have moved his bishop to administer the check!”

“Not bad, Watson; not bad at all! I see you are beginning to think. But why do you have this persistent habit of forgetting that a move may involve a capture?”

Then, of course, I saw it. “Right, Holmes, right. Black’s last move was with the king from a7 capturing a White piece on a8. This piece must have moved before that out of the diagonal from g1 to a7 to uncover check from the bishop. What piece could that be? Why obviously a knight, which had moved from b6 to a8. Thus Black’s last move was from a7 to a8, capturing a White knight.”

“Correct,” said Holmes.

A new thought suddenly occurred to me. “Holmes” I said, “is it really necessary in this problem to be given which side was White?”

“Of course,” replied Holmes. “If we hadn’t been given that information, then a second solution would have been possible: A white pawn could have just promoted to bishop.”

A retro problem for Christmas

Raymond Smullyan, Manchester Guardian 1957

In the above position White has just removed
his king from the board. From which square,
and what were the last two moves?

Please make a note of your solution for your prize competition submission at the end of the Christmas puzzle week. Please do not send in any solutions until all eight sections have been published.

Frederic Friedel

Solution