Puzzles
Seat four married couples around a table so no one sits beside their own spouse
Seat men and women alternately around a circular table, with the women's seats already fixed, so that nobody ends up next to their own husband or wife. For four couples, how many valid ways are there to seat the men? French mathematician Édouard Lucas posed this in 1891 as the 'problème des ménages.'
Reveal the answer
Exactly 2 valid arrangements. The sequence of these counts for larger numbers of couples — 1, 2, 13, 80, 579... — is now called the ménage numbers, and working out a general formula for them took mathematicians decades, tying the puzzle to deep results in combinatorics like the rook polynomial and inclusion-exclusion.