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
Oakley 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 sets him free.
What color was C’s hat, and how did C do his reasoning?

Explanation / Answer

Answer:

C’s hat color was white.

C’s thinking goes as below,

Assume I had a red hat & let us assume B also had a red hat. If so, then A would have been told his hat color. But he couldn’t tell his hat color. So this wasn’t the case.

Now assume that I had red hat and B had a white hat. Then B argued as follows,

“If I(B) had a red hat then A would have correctly guessed his hat color. But the correct fact is that A couldn’t guess his hat color instantly. It implies that I (B) should have a white-color hat.

Since B couldn’t guess his color of the hat. Therefore 2nd supposition is wrong. It tells that C never hat a red color hat. Then hat color of the C is white.

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