The county jail is full. The Sheriff, Anne Oakley, brings in a newly caught crim

Question

The county jail is full. The Sheriff, Anne Oakley, brings in a newly caught criminal and decides to make some space for the criminal by letting one of the current inmates go free. She picks prisoners A, B, and C to choose from. She puts blindfolds on A and B because C is already blind. Next she selects three hats from five hats hanging on the hat rack, two of which are red and three of which are white, and places the three hats on the prisoner’s heads. She hides the remaining two hats. Then she takes the blindfolds off A and B and tells them what she has done, including the fact that there were three white hats and two red hats to choose from. Sheriff then says, “if you can tell me the color of the hat you are wearing, without looking at your own hat, then you can go free.” The following things happen:
1. ‘A’ says that he can’t tell the color of his hat. So the sheriff has him returned to his cell
2. Then ‘B’ says that he can’t tell the color of his hat. So he is also returned to his cell
3. Then ‘C,’ the blind prisoner, says that he knows the color of his hat. He tells the sheriff, and she gets him free.
What color was C’s hat, and how did C do his reasoning

Explanation / Answer

C's reasoning goes as follows:

Suppose I had a red hat and suppose B too had a red hat on. Then A would have been able to tell the color of his hat. Since he couldn't this was not the case.

Suppose I had a red hat, and B had a white hat on his head. Then B could have argued in the following manner:

"If I (now B) had a red hat on my head, then A would have guessed his hat correctly. The fact that he couldn't guess immediately means that I must have a white hat on my head."

But the fact is that B could not guess his hat color. Hence this second supposition is also wrong.
But then C could not have had a red hat on his head => C has a white hat on his head.

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