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In a parallel universe when Neil Armstrong landed on the moon, he found it to be inhabited by a tribe of humanoids. He discovered that:

  1. they were all married
  2. the husbands of 10 of the wives were unfaithful
  3. Each wife knew whether or not any other wife's husband was a cheater, but did not know whether or not her own husband was a cheater
  4. No wife was allowed to tell any other wife that her husband was unfaithful or otherwise. Husbands also did not discuss this but otherwise gossip was gossip …
  5. If a wife discovered her husband was unfaithful she had to throw him out of the house and onto the street at precisely 10am the following day, where he would be visible to all others in the tribe.

Foolishly Neil informed the entire tribe at 11am on the day that he landed that at least one of the husbands was unfaithful. What happened next?


marked as duplicate by Micah, vonbrand, Paul, Joe, J. M. is a poor mathematician Apr 21 '13 at 10:35

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  • $\begingroup$ In case anyone wonders whether (4) allows men to gossip with women about who is unfaithful: it does not. $\endgroup$ – Brian M. Scott Apr 4 '13 at 21:04
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    $\begingroup$ Conspiraciy theorists may ask: Why does the problem require a parallel universe? Because in ours the moon is uninhabited or because in ours the moon landing was faked? $\endgroup$ – Hagen von Eitzen Apr 4 '13 at 21:51
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    $\begingroup$ At noon, one of the wives finds a pair of frilly underwear behind the bed that isn't hers. The next morning, her husband is out on the street. The tribe returns to business as usual, and the 9 other cheaters breathe a sigh of relief. (Or do they?) $\endgroup$ – mjqxxxx Apr 4 '13 at 22:28

That's the famous problem related to the concept of the common knowledge, and the solution is well-known though often leads to arguments of people who don't rely upon it. The hint it to solve the problem by induction: suppose that there is only one guy who is cheating and see what happens. Then think of two guys cheating and try reducing it to the previous case, etc.

See also a very similar problem about blue-eyed guys in my link. Also, here is a post of Terry Tao on this problem.

Since it's a CW post, I decided to do a bit of a search on MSE and found several more examples which talk about blue eyes.


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