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the Sponge Inner circle Atlanta 2771 Posts |
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On Aug 17, 2017, landmark wrote: Look at the part in the Parentheses. I think it is meant to be the same. |
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LobowolfXXX Inner circle La Famiglia 1196 Posts |
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On Aug 17, 2017, landmark wrote: I presented it the way it was presented in a book I bought, and I failed to catch the mistake in the book's presentation - the wives have to not only know about the other husbands, but also that the OTHER wives know about the other husbands. You're right; as posted, it's no good.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley. "...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us." |
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LobowolfXXX Inner circle La Famiglia 1196 Posts |
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On Aug 17, 2017, 0pus wrote: In the 2-wife formulation, the king's statement is relevant; if the king didn't say that one husband had been unfaithful, neither wife would be able to draw an inference. But because of the king's statement, each wife reasons "If my husband were not cheating, then the other wife would know that it was HER husband who was cheating, and she would have killed him on Day 1," then they each kill their husbands on Day 2. This works in a 2-couple universe, when a cheating husband would only have one wife to cheat with. The puzzle as I posted it doesn't work with more than two couples, but if all of the wives know that the other wives all know about the husbands that are not theirs, then it works with any number, and all of the wives will kill their husbands on the same number day as there are couples.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley. "...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us." |
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0pus Inner circle New Jersey 1739 Posts |
I think that even in the 2-couple universe, it would be a required condition for each wife to know that the other wife knows about the husband that is not hers.
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LobowolfXXX Inner circle La Famiglia 1196 Posts |
Or that the only person that someone can cheat with is the other of their couple. If Wife 1 can only cheat with Husband 2, and Husband 1 can only cheat with Wife 2, then it works.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley. "...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us." |
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0pus Inner circle New Jersey 1739 Posts |
Even with your proposal, why couldn't each wife have cheated with the other's husband, but still believe that her own husband is faithful? So Wife 1 knows that Husband 2 is unfaithful (because he has been unfaithful with her), and Wife 2 knows that Husband 1 is unfaithful (because he has been unfaithful with her), but neither knows that her own husband has been unfaithful on these conditions. One would have to add a condition that addresses the unfaithfulness of the wives (like each wife has also been unfaithful), no?
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