Prisoners and Hats and a Jungle, Oh My!

The Puzzler

RAY: At certain jungle prison, there are 30 prisoners who have been sentenced to be executed. Yikes! The warden, of course, has the power to pardon, and he decides to play a little game. Of course he does, right?

He announces to the prisoners that he will stand all of them in a straight line, with Prisoner Number 1 facing the wall, and the remaining prisoners lined up behind him, with each one able to see the heads of those prisoners in front of him, but not his own head of course, or those heads behind him. Kinda like standing in line at the men's room at the ol' ballpark.

Next he will place either a white or a black hat on each prisoner's head, starting at the back of the line, and a guard will then ask each prisoner, starting at the back of the line, we'll call this Prisoner Number 30, to identify the color of his own hat.

Remember, Prisoner Number 30, the one at the back of the line, can see all the other hats and prisoners in front of him. Number 29 can see the 28 hats in front of him, et cetera, et cetera, et cetera, but Prisoner Number 1 can see what?

TOM: Bupkis!

RAY: Exactly right. Of course, each prisoner can hear each of his fellow prisoners attempt to identify the correct color of his hat. When asked the color of his hat, a prisoner can say only one of two words: black, or white. That's it. Now he explains this to the prisoners, and immediately they come back and say, "Hey, come on man, give us a fighting chance! If we've only got a 50/50 chance of making it here, give us something we can do to help improve the odds."

He says, "Alright, alright, look, I hate to execute complainers, so I'll give all of you one hour to talk among yourselves and come up with a strategy. After that, silence. And remember, no funny business. Each one of you is allowed, when asked, to utter one word and one word only, either black or white. If I suspect anything is amiss, you all die."

So the question is, is there a strategy that they can use that will improve their chances, and if so, what is it?

Notice, by the way, that I did not say how many black or how many white hats there were; it doesn't matter.

Think you know? Drop Ray a note!

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