I am not sure whether this qualifies, but anyway there is the following coin problem
Twelve coins are identical in appearance, but one coin is either heavier or lighter than the others, which all weigh the same . Identify in at most three weightings the bad coin and determine whether it is heavier or lighter than the others using only a pan balance.
There was a solution given by the Blanche Descartes collective in the form of a poem published in the magazine of the CU mathematical society (the reference is Nr.13, 1950)
F set the coins out in a row
And chalked on each a letter, so,
To form the words "F AM NOT LICKED"
(An idea in his brain had clicked).
And now his mother he'll enjoin:
MA DO LIKE
ME TO FIND
FAKE COIN
Ian Stewart has written on this in an article called To Find A Fake Coin in the SIAM.