Puzzles based on the chessboard have been popular since the medieval era, when chess itself first became widely popular. In recent times, a puzzle genre has emerged revolving around the rules of chess, as seen in the collection by the late Raymond Smullyan, The Chess Mysteries of Sherlock Holmes (1979), where the puzzles are framed as dialogues between master fictional sleuth Sherlock Holmes and his assistant Watson: “Black moved last, Watson. What was his last move—and White’s last move?” Without giving away the answer, which I leave up to the reader, suffice it to say that there is a trick here—a piece (like a White Bishop) was blocking the attack, and White moved another piece (like a Rook) out of the way, resulting in a discovered check.

Solving such puzzles involves an integrated use of spatial reasoning (determining where the pieces are on the board and how they can move about) and insight thinking (discovering the trick via an “Aha!” insight). To put it colloquially, in such puzzles, spatial reasoning “meets” insight thinking. Some chessboard-based puzzles, however, might enlist these two processes in an entangled way instead, with the insight resulting from disentangling the puzzle from how it describes a situation spatially.

A classic example is the so-called mutilated chessboard problem, invented by philosopher Max Black in his 1946 book Critical Thinking. It can be paraphrased as follows:

If two opposite corners of a standard 8-by-8 checkerboard are removed,........

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