SOLUTION: Can you help me. I need to how to do this logic problem, step by step. Three geniuses stand in a file (one behind the other). Each can see only to the front, so the rear person

Question 136137: Can you help me. I need to how to do this logic problem, step by step.
Three geniuses stand in a file (one behind the other). Each can see only to the front, so the rear person can see the middle and the front, the middle person can see the front, and the genius in the front cannot see anyone.
You have five hats. Two are white, and three are red. You blindfold the three geniuses, who are utterly truthful, and put a hat � at random � on the head of each. Then you hide the other two hats and remove the blindfolds.
You then ask each genius to name the color of his hat (which he cannot see).
The rear one says "I don't know." The middle on says, "I don't know." Then the front one says, "I know."

WHAT COLOR IS THE FRONT GENIUS' HAT??????

Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
The back genius doesn't know. How can this be? If both the middle and the first people were red, the back would know his was white. He doesn't know. So the options for the two hats he sees are either : 1 red/1 white, or 2 white.

The middle genius doesn't know. He logically decides the first guy saw either 2 whites, or a white and a red. Since he can see the person in front of him, he must be seeing a white hat on the first genius. Because if he saw a red hat on the first genius, he (the second genius) would have to be wearing a white one. And since he is a genius, he would say 'i know'.

The first genius uses the logic above to say "I know". And when they ask what color, she will say "white".
Make sense?
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