One sailor wakes up in the night, and since he doesn't quite trust the others, he decides to take his share. He divides the coconuts into five piles. Finding one coconut left over, he gives it to a monkey watching nearby. He then hides his pile and pushes the remaining four piles into one large pile and goes back to sleep.
Each of the other four sailors wakes up in the night and repeats the actions of the first sailor. After dividing the pile, each finds one extra coconut, which he gives to the monkey.
In the morning, the pile of coconuts is noticeably smaller, but since each is at fault, no one mentions it. They divide the remaining coconuts evenly among themselves.
How many coconuts did the five men originally gather?
Source: 1. Many sources. 2. Original.
(I answered "1", and he asked for a little more interesting solution.)
The solutions are:
The general formulae are: