Five sailors, a monkey, and a pile of coconuts nobody can split fairly
Five sailors and a monkey are shipwrecked and spend a day gathering one big pile of coconuts, planning to split it evenly come morning. In the night, each sailor in turn secretly wakes, divides the pile into five equal shares with exactly one coconut left over for the monkey, hides his own fifth, and pushes the rest back together. By morning the remaining pile splits perfectly into five, with nothing left over. What's the smallest number of coconuts the pile could have started with?
Reveal the answer
3,121 coconuts. The slickest route in: imagine adding 4 'blue' coconuts to the pile at the very start, one riding unnoticed in each fifth every time it's divided — now every split is exact, five times over, so the padded pile must equal 5^5 = 3,125. Subtract the 4 blue coconuts back out and you get 3,121. The puzzle traces to the 9th-century Indian mathematician Mahavira, but exploded into fame after Ben Ames Williams's 1926 short story 'Coconuts' ran unsolved in the Saturday Evening Post, triggering over 2,000 letters from readers demanding the answer.