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Four Hats

Problem

A teacher shows three clever boys a pile of four hats: two blue and two red. They are all blind-folded, each given a hat to wear at random, and lined-up in a line so that they are all facing towards a wall. When the blind-folds are removed, the first boy can only see the wall, the second boy can see the first boy, and the third boy can see the first two boys. None of the boys can see the colour of his own hat.

The first boy to correctly shout out the colour of his own hat will have no homework that evening. However, if he guesses incorrectly, he will have to complete the other boy's homework.

Which of the boys, 1 to 3, is most likely to correctly deduce by logic alone the colour of his hat?

Problem ID: 337 (16 May 2008)     Difficulty: 2 Star

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