Here is a mind-numbing logic puzzle from *Futility Closet*.

“A puzzle by H.A. Thurston, from the April 1947 issue of *Eureka*, the journal of recreational mathematics published at Cambridge University:

Five people make the following statements:—

Which of these statements are true and which false? It will be found on trial that there is only one possibility. Thus, prove or disprove Fermat’s last theorem.”

Normally I would forgo something this complicated, but I thought I would give it a try. I was surprised that I was able to solve it, though it took some tedious work. (Hint: truth tables. See the “Pointing Fingers” post regarding truth tables.)

One important note. The author is a bit cavalier about the use of “Either …, or …”. In common parlance this means “either P is true or Q is true, *but not both*” (exclusive “or”: XOR), whereas in logic “or” means “either P is true or Q is true, *or possibly both*” (inclusive “or”: OR). I assumed all “Either …, or …” and “or” expressions were the logical inclusive “or”, which turned out to be the case.

See the Fermat’s Last Theorem Puzzle

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