Hint to Puzzle #39: 100 Prisoners in a Line, Red & Blue Hats and the Executioner

39. An executioner lines up 100 prisoners single file and puts a red or a blue hat on each prisoner's head. Every prisoner can see the hats of the people in front of him in the line - but not his own hat, nor those of anyone behind him. The executioner starts at the end (back) and asks the last prisoner the colour of his hat. He must answer "red" or "blue." If he answers correctly, he is allowed to live. If he gives the wrong answer, he is killed instantly and silently. (While everyone hears the answer, no one knows whether an answer was right.) On the night before the line-up, the prisoners confer on strategy to help them. What should they do?

This puzzle is pretty tough. There appears to be no mechanism by which useful information can be passed forward, whilst also allowing the person giving it to survive.

Whilst thinking about it it may help to consider the following smaller set.

prisoners in a row wearing hats red blue red red blue

The only clue I can think of is a big one. I struggled with this puzzle and I saw one word on a page and the answer was obvious. So big is the clue that I'm going to hide it for now until you are sure you want it...

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