10 prisoners are called before an executioner. The executioner says: “Tomorrow, I will put you in a line, front-to-back. So the person in front can see no one else, and the person in back can see everyone else in front of him. I shall then place either a white hat or a black hat on your head. I will begin at the back of the line and ask you what color your hat is. You may make no signal or say anything other than ‘WHITE’ or ‘BLACK’. If you get it right, you will be freed; if you fail, I will execute you.”
The men go back to their shared cell and deliberate the problem, when one speaks up and says, “I know a way is guaranteed to save 9 of us, and will give the other man a 50/50 shot.”
What was his method?
To be clear on the rules:
* Each man can see all of the hats on the men in front of him, but not his own nor the men behind him.
* Each man may say only “white” or “black” — no kicking the guy in front of him, no indicative pauses, etc. Think of this like a binary-answering situation.
* There is no quaranteed even distribution of the hats.
