Tuesday, May 15, 2007

5/15/07 Hat Problem

This ain't your grandma's logic problem. Here's a new twist on a hat problem. Can you give an optimal solution?

Three players enter a room and a red or blue hat is placed on each person's head. The color of each hat is determined by a coin toss, with the outcome of one coin toss having no effect on the others. Each person can see the other players' hats but not his own.

No communication of any sort is allowed, except for an initial strategy session before the game begins. Once they have had a chance to look at the other hats, the players must simultaneously guess the color of their own hats or pass. The group shares a hypothetical $3 million prize if at least one player guesses correctly and no players guess incorrectly.

3 comments:

No Longer Neighbor Natalie said...

I'm usually wrong about a lot of things. But, I'm going to take a stab at this "logic" problem:

First off, in order for the players to share any of the winnings, each has to guess correctly -- "At least one player guesses correctly + no one guesses incorrectly," meaning EVERYONE has to guess right, right?

Secondly, what strategy? Why meet and confer? "The color of each hat is determined by a coin toss." Each event is mutually exclusive. It's chance; it's not logic. Take your best guess! The probability that you guess your own color right is 1:2. The probability that everone goes home a millionaire is, like, 1:4 (I think).

So, what was the problem? No, wait, the "optimal" solution, you asked?

Everyone should bring a lucky troll. You know, something with nylon hair and a plastic rhinestone for a belly-button.

No Longer Neighbor Natalie said...

Er, just a side note: I calculated the last probability wrong. It's a glaring error. I think I figured out the permutation, or something like that... in which case, I'm probably still wrong because I'm not any good in Math.

Nevertheless, I hope my "solution" still holds water, since it's not numbers based.

Neighbor Natalie said...

On that note, did you know a roll of quarters costs $10.00?! Cripes.