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349 logic/smullyan/painted.heads.p




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This article is from the Puzzles FAQ, by Chris Cole chris@questrel.questrel.com and Matthew Daly mwdaly@pobox.com with numerous contributions by others.

349 logic/smullyan/painted.heads.p


While three logicians were sleeping under a tree, a malicious child painted
their heads red. Upon waking, each logician spies the child's handiwork as
it applied to the heads of the other two. Naturally they start laughing.
Suddenly one falls silent. Why?

logic/smullyan/painted.heads.s

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.

 

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