# Three students sit in a circle in a classroom

November 24, 2016

Three students sit in a circle in a classroom. Each student is wearing a hat, either red or white. A student can see the hat (and identify the colour) on the heads of the other two students but on his or her own head. Suppose all the students are wearing a white hat. If the teacher asks if any student can identify the colour of the hat on his or her own head, what answer does each student give?
Consider the situation in question #1. Now suppose the teacher makes the statement “there is at least one white hat in the room”. (a) If the teacher asks student 1 (in front of the other students) if they know the colour of the hat on their head, what answer does the student give? (b) If the teacher then asks student 2 (in front of the other students) if they know the colour of the hat on their head, what answer does the student give? (c) If the teacher Önally asks student 3 if they know the colour of the hat on their head, what answer does the student give? (d) How would the problem in question 1 and this question change if 2 students are wearing white hats and 1 student is wearing a red hat?

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