So, I would have gotten a lot more done these past few days if lnhammer hadn’t casually tossed the following math problem at me:
Five men and a monkey are stranded on a desert island. Figuring they might be there a while, they gather up all the coconuts they can find, but are so tired afterwards they decide to wait until morning to divide the coconuts up.
Only one of the men wakes up in the middle of the night, and decides he doesn’t wait until morning to take his share. He divides the coconuts into five equal piles. But there’s one coconut left over, so he gives that one to the monkey. He then hides his share and goes back to sleep.
Then a second man wakes up, has the same thought. He divides the remaining coconuts into five equal piles. Has one left over, gives it to the monkey. Hides his coconuts, goes back to sleep.
And so on for the third, fourth, and fifth men, each of whom in turn divides the remaining coconuts up, has one left over which he gives to the monkey, hides his share, and goes back to sleep.
In the morning, the men together divide the remaining coconuts into five equal piles, and have none left over. (Much to the monkey’s annoyance.)
The question being, of course–how many coconuts did they start with? (Well, I have some other questions about this whole setup, too, but the mathematical question is, how many did they start with. :-))
This problem is of course much harder than it seems, and has been diverting valuable brain cells from their appointed tasks for days.
But this morning I figured out the answer. Hah!
But I’m not telling. Because, like, why should I be the only one whose brain hurts?