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Jan10-11, 06:30 AM
Sci Advisor
P: 2,470
Yes, I should have stated that explicitly. I wasn't focusing on the problem too much. Thought more people would have seen it before in one form or another.

Alright. Let me just go through all of the logic, hopefully, making all implicit assumptions explicit in the progress.

Suppose there is only one unfaithful wife. A philosopher whose wife she is learns that not all wives are faithful, and he knows all other philosopher's wives are. So it must be his wife that is unfaithful. He goes home and kills himself. On the next day, all others learn of that event.

Suppose there are two. The two philosophers whose wives they are know of each other's wives. So they know that if she's the only one, her husband can make the deduction described above and will commit suicide. When both of them show up the next day, they both conclude that there are at least two unfaithful wives, and since each of them is only aware of one, they go home and commit suicide. Again, all of the rest learn about it on the next day.

Suppose there are three. Then the philosophers whose wives they are are aware of two, and relying on logic above after two days can verify that there are more than two. So they kill themselves.

Similar logic applies to any other quantity of unfaithful wives.

The assumptions used are that all information is exchanged during daily meeting, they all know everything about everyone's wife but their own, and they know that discovery of unfaithfulness would result in suicide. And yes, when given as an actual problem, these things should be stated explicitly for the problem to be well-posed.