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The Magic Cafe Forum Index » » Puzzle me this... » » Th Unfaithful Husbands (0 Likes) Printer Friendly Version

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the Sponge
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Quote:
On Aug 17, 2017, landmark wrote:
Quote:
On Aug 17, 2017, the Sponge wrote:
Here is an explanation:

http://www.ritambhara.in/cheating-husband-puzzle/


Thanks. Condition 2 in that puzzle seems significantly different from Lobo's formulation; or perhaps he meant it and it wasn't clear (at least to me).

Look at the part in the Parentheses. I think it is meant to be the same.
LobowolfXXX
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Quote:
On Aug 17, 2017, landmark wrote:
Quote:
On Aug 17, 2017, the Sponge wrote:
Here is an explanation:

http://www.ritambhara.in/cheating-husband-puzzle/


Thanks. Condition 2 in that puzzle seems significantly different from Lobo's formulation; or perhaps he meant it and it wasn't clear (at least to me).


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."
LobowolfXXX
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Quote:
On Aug 17, 2017, 0pus wrote:
Quote:
On Aug 15, 2017, LobowolfXXX wrote:
. . . each wife believed their own husband was faithful, but knew that the other 39 were not.


What new information does a wife have when the king says

Quote:
"I know that at least one husband has been unfaithful . . . ."


What new information does this statement provide to any wife? She already knows that at least one husband has been unfaithful, but not her own. Does the king's statement provide any reason for any wife's changing her belief that her own husband has been faithful? Does the inaction of any wife (to kill her husband) give rise to a conclusion that her belief in her own husband's fidelity must be wrong?



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."
0pus
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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.
LobowolfXXX
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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."
0pus
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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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