colored hats

[Toadman]

Please help me word this better if it needs it. Suppose there are 64 men stand in a single file line and a hat they can not see will be placed on their head. The hats will be either black or white. The man at the end of the line can see everyone else hat and is allowed to go first. The rules are you can only say one word "black" or "white" he may not signal the others in any other way. The others can hear the answers of everyone behind them as they go. knowing this what is the best strategy the men could use to get the most amount of correct guesses. There is no pattern to which the hats are arranged and there can be the same amount of black and white or one black and the rest white that is unknown. Also I am having trouble figuring out how to search to make sure I do not post the something someone else has already posted. Sorry if I do.

[Toadman]

The man that is last in line (but goes first) will say "Black" if he sees an odd number of black hats and "white" if he sees an even number of black hats. Each man can count the number of black hats in front of them and by knowing if the last person sees odd or even they will know the color of their hat.

[bonanova]

It's an excellent puzzle. You can find some extended discussion of it here.

To locate previous posts, enter key words in the search box -- upper right corner, just under your name.
I found this link by entering the words "hats death row"
I happened to remember that "death row" was in the title.