A Fishermen, Sand and Hats Puzzle

If you’re with a group of people and/or bored and looking for something to do, give this little hat puzzle a whirl. It’s one of those ‘think logically’ questions – good luck!

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A mean local has buried four fishermen up to their necks in sand on the beach at low tide for keeping their fishing spot a secret from him. Three have been buried facing the same way, and another has been buried facing them, but the other side of a giant sand dune. He put a hat on each of their heads and told them that one of them must shout out the correct color of their own hat or they will all be drowned by the incoming tide. They are not allowed to speak to each other or turn their heads, and they don’t see the colour of the hat when they are placed on their heads. He’s given them 10 minutes to do this.

Fisherman A and B can only see the sand dune. Fisherman C can see that fisherman B has a white hat on. Fisherman D can see that C has a black hat, and B has a white hat. The fisherman have been told that there are four hats, two white and two black, so they know that they must have either a white or a black hat on. Who shouts out the colour of their hat, and how do they know?

Scroll down for the solution….

Solution

Fisherman C shouts out.

Fishermen A and B are in the same situation – they have no information to help them determine their hat colour so they can’t answer. C and D realise this. Fisherman D can see both B and C’s hats. If B and C had the same colour hat then this would let D know that he must have the other colour. But he can’t be sure.  When the time is nearly up, C realises that D isn’t going to answer because he can’t. C realises that his hat must be different to B’s otherwise D would have answered. C therefore concludes that he has a black hat because he can see B’s white one.