Here's a toughie. A room full of prisoners is given hats, whose color only the others can see. And just to be different, let's say they are yellow or green. No communication is permitted. At a signal, given by the warden, the prisoners must simultaneously shout out the color of their own hat. Those who guess wrong are subsequently executed.

Beforehand, the prisoners meet to determine a strategy -- a set of rules, not necessarily the same for each prisoner -- that will guarantee the greatest number of survivors. As an added wrinkle, the warden may attend the meeting and then use his knowledge of their strategy when he chooses the colors of their hats.

If there are 100 prisoners, how many can be assured of surviving?

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## bonanova

Here's a toughie. A room full of prisoners is given hats, whose color only the others can see. And just to be different, let's say they are yellow or green. No communication is permitted. At a signal, given by the warden, the prisoners must simultaneously shout out the color of their own hat. Those who guess wrong are subsequently executed.

Beforehand, the prisoners meet to determine a strategy -- a set of rules, not necessarily the same for each prisoner -- that will guarantee the greatest number of survivors. As an added wrinkle, the warden may attend the meeting and then use his knowledge of their strategy when he chooses the colors of their hats.

If there are 100 prisoners, how many can be assured of surviving?

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