Five sailors, a pile of coconuts, a monkey, and a division that never comes out even
Five sailors are shipwrecked with a pile of coconuts. In the night, each sailor in turn wakes up, divides the pile into five equal piles with exactly one coconut left over, which he tosses to a monkey, then hides his own pile and goes back to sleep, unaware the others did the same. In the morning, the remaining pile divides evenly among all five sailors, again with exactly one coconut left for the monkey. What is the smallest number of coconuts that could have started the pile?
Reveal the answer
3,121 coconuts. This puzzle, published by Ben Ames Williams in the Saturday Evening Post in 1926, became notorious for drawing thousands of reader letters, many containing a workable but far larger answer; the true minimum involves allowing the trick of imagining negative coconuts during the algebra, a method Martin Gardner later popularized in his 'Mathematical Games' column. Paul Dirac is said to have found the negative-coconut trick independently and almost instantly.