Here’s a tough one from a magazine back in the ’50’s. If anyone here can solve it without using brute force I will be very, very impressed. I might even bestow upon you all of my designations:
5 men are shipwrecked on a desert island. On the first day, they begin collecting food. The only food source on the island is coconut. The men spend the whole day collecting coconuts and at the end of the day have quite a nice pile. Exhausted, they all lie down to sleep.
After the others have fallen asleep, one man realizes that any of the others could steal from his “share” while the group is sleeping. So he gets up and divides the coconuts into 5 even piles. But there is one extra coconut – so he gives it to a monkey who is jumping around in the nearby tree. The man takes his pile and hides it, moves the other 4 piles back together to hide what he did, and then goes to sleep.
A short while later, one of the other men wakes up, and reasons the same as the first man, that he had better take his share now so that he does not get cheated. He divides the big pile into 5 even ones, but there is one left over. He gives it to the aforementioned monkey. He then takes his pile, pushes the other 4 piles back into 1, hides his and goes back to sleep.
A short while later, another man wakes up and does the same as the man before him. Again there is an extra coconut when he divides by 5, which he gives to the monkey. This process continues until every man has done the same deed. That said, each man now has a hidden pile of coconuts, there is a diminished pile left for the community, and the monkey has 5 coconuts.
In the morning, they all wake up and divide the pile into 5. This time, it divides evenly and the monkey walks away dejected. Each man must have noticed that the pile was much smaller than last night, but his guilt prevented him from bringing up the subject.
How many coconuts were there originally, and how many were there when it was finally divided?
There are of course mulitple solutions to this (I found over 100), but they are all multiples of the minimum solution. So there is really only one solution of importance – the minimum. Using brute force requires plenty of skill in this problem so it is legitimate to answer it that way, but an elegant solution would be amazing!