Five brigands, 200 doubloons, and thousands of ways to split them
Five Spanish brigands split exactly 200 doubloons between them. Someone notices something odd: if Alfonso had 12 times his actual share, Benito 3 times his, Carlos the same amount he actually had, Diego half his, and Esteban a third of his, the total would still come to exactly 200 doubloons. Every man held a whole number of coins, at least one. How many different ways could the 200 doubloons actually have been split among the five?
Reveal the answer
6,627 different ways. Henry Dudeney traced the puzzle back to the Renaissance mathematician Tartaglia (d. 1559), and used his own solution to correct a French editor's published claim of 6,639 solutions — the true count is 6,627. From Henry Dudeney's Amusements in Mathematics (1917), puzzle No. 133, "The Five Brigands."
— Henry Dudeney, Amusements in Mathematics — Puzzle No. 133, "The Five Brigands," 1917