Five sailors, a monkey, and a pile of coconuts that never divides evenly
Five shipwrecked sailors gather a pile of coconuts to split in the morning. In the night, each sailor in turn wakes, divides the pile into five equal piles with exactly one coconut left over, gives that one to a monkey, hides his fifth, and goes back to sleep — without knowing the others did the same. By morning, the sailors split what's left five ways with nothing left over. What's the smallest pile they could have started with?
Reveal the answer
3,121 coconuts. Working backwards through five rounds of 'remove one, keep four-fifths' shows 3,121 is the smallest starting pile where every nighttime division leaves exactly one coconut for the monkey and the final morning split comes out exactly even. Ben Ames Williams published the puzzle as a short story in the Saturday Evening Post in 1926, and the magazine was reportedly flooded with over 2,000 letters demanding the answer.