The one who fell silent, presumably the quickest of the three, reasoned that his head must be painted also. The argument goes as follows. Let's call the quick one Q, and the other two D and S. Let's assume Q's head is untouched. Then D is laughing because S's head is painted, and vice versa. But eventually, D and S will realize that their head must be painted, because the other is laughing. So they will quit laughing as soon as they realize this. So, Q waits what he thinks is a reasonable amount of time for them to figure this out, and when they don't stop laughing, his worst fears are confirmed. He concludes that his assumption is invalid and he must be crowned in crimson too.

This puzzle has been attributed to Alonzo Churchin the 1930s.

This puzzle can be scaled up to any number of logicians and then is analogous to the "common knowledge" problem.

SEE ALSO "priest"

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