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Three men are sitting in a room. They are blindfolded and told that either a red or a green hat will be placed on their heads. A red hat is placed on each head The blindfolds are removed and the men are told to raise their hand if they can see a red hat Each man raises his hand. They are then told that when they know the colour of their own hat to leave the room. After a short pause, one of the men leaves the room. How did he know he had a red hat on?

He took it off and looked at it.

Or: a red hat will be placed on all their heads or a green hat ditto.

If he has a green hat, one of the others will work out that he has a red hat. As neither does, he must have a red hat too.

The fact that nobody guesses right away indicates that all have red hats. Since everyone can see at least one red hat (all hands are raised), there must be at least 2 red hats. Suppose there were 2R, 1G. Whoever saw a red and a green would know theirs was red and say so. Since everyone sees two reds there can be no guess based on that scenario, so 2R 1G is not possible. Therefore all hats must be red.

Well done Chrise and kilgour trout. I always suspected you were both pretty brainy! All the best

Thanks, farr - for the problem and the compliment!