Some time ago, I chanced upon the following puzzle:

Five men find themselves shipwrecked on an island, with nothing edible in sight but coconuts, plenty of these, and a monkey. They agree to split the coconuts into five equal integer lots, any remainder going to the monkey.

Man 1 suddenly feels hungry in the middle of the night, and decides to take his share of coconuts at that very moment. He finds the remainder to be one after division by five, so he gives this remaining coconut to the monkey and takes his fifth of the rest, lumping the coconuts that remain back together. A while later, also Man 2 wakes up hungry, and does exactly the same thing: takes a fifth of the coconuts, gives the monkey the remainder, which is again one, and leaves the rest behind. So do men 3, 4, and 5. In the morning they all get up, and no one mentions anything about his coconut-affair on the previous night. So they share out the remaining lot in five equal parts finding, once again, a remainder of one left for the monkey. Find the initial number of coconuts.^{1}

I won’t give you the answer, so you can enjoy finding it by yourself. The solution is not trivial, for you have to solve a Diophantine equation, but in the end it is not too much complicated. Obviously, there is an infinite number of possible solutions, but the problem implicitly asks for the smallest one.

The puzzle, * per se*, is not very intriguing, but what makes it interesting is a story that usually goes with it. Continue reading