## May 7, 2005

### brain teasers

I heard a brilliant brain teaser this week. Here it is. I'll post the answer later (I still have to proof the answer to make sure it's correct)
5 pirates find a treasure chest filled with 500 gold coins. They can't agree how to split it up - each finding a reason why they should get more. They finally decide to a process to split the treasure. One of the pirates will go first. He will propose a way to split the treasure and then all the pirates will vote. If there is a majority they split up the treasure. If there is no majority the pirate who made the suggestion walks the plank. Then the next pirate suggests a way to split the treasure among the remaining 4 pirates and they vote again. If there is a majority they split up the treasure. No majority gives him the plank. And so on.

Note that any given pirate doesn't want his friend to die so if there are two equal economic outcomes for him then he'll pick the one that doesn't kill his friend. If he can capture another gold coin, however, he'll vote to give him the plank.

How is the money eventually split up and who is dead?

While I'm here I'll give you my favorite brain teaser:
A census taker visits a house in the neighborhood he's canvassing. A man answers. The following conversation occurs:

Census-taker: "How many kids do you have?"
Man: "3"
Census-taker: "How old are they?"
Man: "Well the product of their ages is 36"
Census-taker: "Okay"
Man: "And the sum of their ages is my house number"
Census-taker: [looks up at number] "That's not enough information"
Man: "Oh the oldest likes bananas"
Census-taker: "Thanks"

How old are the man's kids?