On Tuesday 06 January 2004 08:56, Eugene Salamin wrote:
--- Joshua Singer <singer@stanford.edu> wrote:
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
This can't be right. The information provided by the traveler was already known to everybody. In the case of the problem of the unfaithful wives, the king issues an edict, which starts the clock ticking.
Gene
Of course the problem is to determine under what condition this occurs. Certain conditions can be eliminated --- Such as single person with a red dot hears the statement and reports it to everyone else. If we choose the right group of people to be present when the traveler makes the statement, the the solution is more obvious. All the problem asks is that we explain how it happened. It is crucial that everyone knows the color of everyones dot. For instance, if only one person had a blue dot and they heard the statement either directly or indirectly, they would have to leave town. Now consider the case of two people with blue dots who hear it directly. Regards Otto otto@olympus.net
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