I remember once reading a proof that a square, four-legged table could always stand on a surface, even an uneven one, with all four of its legs touching the ground. ( Unfortunately, the margin of this cut-text is too small to contain it. )
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dotaturls:
Romantic cryptology - if XKCD were an academic paper...?
A paper on how A and B (Alice and Bob, or Albert and Brenda, or Alice and Brenda, or Albert and Bob) can determine whether they love each other, without finding out the other person's choice in case the love is not mutual. (As in, if you have a crush on someone, how to find out whether they have a crush on you too without revealing your crush to them in case they don't requite it.)
A bit whimsical due to its subject matter, but interesting from a mathematical standpoint.
branchandroot