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Classic Five-Hat Problem (Answer)
Oil and Vinegar Problem (Answer)
Game Show Problem (Answer)

If no.3 can see two red hats, he will know that he is wearing white. However, he cannot answer, and so both no.1 and no.2 now know that he must be seeing at least one white hat.

If no.2 can see a red hat, he knows that he himself must be wearing white. However, he is also unable to answer, so no.1 is able to deduce that he, no.1, is wearing white.

There is also a four-hat version of this, but it works rather differently. If you wish to, try to make head or tail of this article, which describes a number of variants.

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