As it was originally told to me . . . A traveler passes through a small village, each of whose inhabitants has a single colored dot on his or her forehead. Some have a blue dot, some have a red dot, some have a green dot, etc. Each person can see every other person's dot, but cannot see his own. Because the village is small, every person knows the color of every other person's dot, except his own. It is taboo in the village to know the color of one's own dot. The village's strict rule is that anyone discovering the color of his own dot must leave the village within 24 hours, never to return. As the traveler passes through, he casually remarks, "Some people in this village have blue dots". Ten days later, the ten people from the village who had blue dots have all vanished. The problem is to explain how the departure of the ten people occurred. JSS asimovd@aol.com wrote:
Scott asks:
<< ... Then two mathematicians iterate for awhile, A: I can't deduce the answer. B: Neither can I. A: I still can't deduce the answer. ...
and after a few rounds of this one of them can deduce the answer.
Can anyone supply some puzzles of this flavor? (without answer :-)
I vaguely recall one of this type (in a 1958 book, "Puzzle-Math", by G. Gamow & M. Stern) which concerned determining which wives were cheating on their husbands, but I can't recall the details -- except that it took 40 days to deduce who the cheaters were.
The book is, I fear, out of print, but many local libraries may have copies.
Dan Asimov
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