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Puzzle Details

Three people are buried in the sand all facing forwards with their heads above ground.

Each person has a hat placed on their head selected from a bag containing 3 red hats, and 2 black hats, and they knew the possible hat choices.

They cannot turn around to see those behind them.

The person at the back is asked what hat they are wearing. They reply 'I do not know'. The middle person is asked what hat they are wearing. They also reply 'I do not know'. The person at the front is then asked what hat they are wearing. They reply 'I am wearing a red hat'.

How did they know?

[Ref: ZSAU]

Since the person at the back could not determine their own hat, this means that the front two people could not both have been wearing black hats and that, therefore, there must be at least one red hat on the two front people.

Therefore the middle person must not be able to see a black hat otherwise they would know they had a red one on.

Therefore the front person must be wearing a red hat - which finally they deduce. Interestingly, the other two can never determine their own hats.

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