[irchans]

This is one of my favorite puzzles.

You and nine friends are given the opportunity to play a game and win some money. You are all told the rules of the game ahead of time and you can discuss your strategy before the game begins.


All of you will be placed in a line and then ten hats will be placed on your heads. No person will see the color of his own hat. The 10th person will see the color of the 9 hats ahead of him. The 9th person will see 8 hats.... Each person, starting from the 10th in line, will be given a chance to guess the color of his own hat. Every person in the line will hear the guesses of the previous guessers. After all the guesses have been made, every player will be paid one dollar for each correct guess. (i.e. if 5 people guess their hat color correctly, all ten players will recieve $5.)

1) If you and your friends are told that all the hats will be black or white, what is a good strategy for maximizing the average amount of money won.

2) If you and your friends are told that all the hats will be red, black, or white, what is a good strategy for maximizing the average amount of money won.


PS: If you post an answer, please put the word "answer" or "guess" in the subject line so that you don't spoil the fun for the other readers.