Question

Three men are buried in the sand all facing forwards with their heads above ground. Each man has a hat placed on his head selected from a bag containing 3 red hats, and 2 black hats, and the men knew the possible hat choices. The men cannot turn around to see the men behind them. The man at the back is asked what hat he is wearing. He replies 'I do not know'. The middle man is asked what hat he is wearing. He also replies 'I do not know'. The man at the front is then asked what hat he is wearing. He replies 'I am wearing a red hat'. How did he know?

Answer 1

Since the man at the back could not determine his own hat, this means that the front two men could not have been wearing black hats and that, therefore, there must be at least one red hat on the two front men. Therefore the middle man must not be able to see a black hat otherwise he would know he had a red one on. Therefore the front man must be wearing a red hat - which finally he deduces. Interestingly, the other two can never determine their own hats.