Lets look at this from an outsiders point of view... From this new perspective there are only three scenerios --- 1 blue hat in the group, 2 blue hats in the group, and 3 blue hats in the group

• One blue hat - Guy wearing the blue hat sees two white hats, jumps up immediately and yells "BLUE" - Time to play 10 seconds.
• Two blue hats - One of the guys wearing a blue hat realizes that if his own hat was white, the other guy would have yelled "BLUE" 10 seconds into the game. Since this didn't happen, his own hat must be blue. Time to play: 5 minutes.
• Three blue hats - Someone realizes that if his own hat was white, one of the other two would have jumped up and yelled "BLUE" at the 5 minute mark. Since that didn't happen, his own hat must be, "BLUE!" - Time to play 20 minutes.

-Blake

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