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LobowolfXXX
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In a small town long ago, there lived 40 married couples (M/F) and an unmarried king. All 40 of the husbands were cheating on their wives, and each wife believed their own husband was faithful, but knew that the other 39 were not.

One day, the king decreed that to punish the husbands for their wickedness, any wife must kill her husband at noon on the day following any day she learned that her husband was unfaithful. He said, "I know that at least one husband has been unfaithful, and something must be done!"

Assuming the wives were perfect logicians and loyal, degree-following subjects, what, if anything, happened next, and when?
"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."
P.L.Green
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Nothing until day 40, when all wives at once killed their husbands. ;o)
Can you keep a secret?.....So can I ;o)
0pus
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Lobo,

At some time, will you provide the answer and explanation? If so, when?
LobowolfXXX
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P.L is correct, and it's easiest to understand by considering what happens when there's a smaller number. Let's say there was one couple. The wife knows that her husband is cheating, so the next day, she kills him. (She knows because the king said there was at least one cheater).

Now say there are two couples. On day 1, nothing happens, because each wife thinks the king was talking about the other wife's husband. But each wife expects that the other wife will kill her husband, for the same reason that the husband gets killed in the exam when there's one unfaithful husband.

So on day 2, both wives are surprised. Then each realizes that the only reason the other wife didn't kill her husband is that there is uncertainty, which can only arise from the fact that her own husband is cheating, too. So on day two, the both kill their husbands.

With 3 wives, each expects that the other two will be killed on day 2, for the reasons given anove. Then it dawns on each kf them, and on day 3, all three kill their husbands.

And so on...so in my example, all is well for 49 days, with each wife blissfully ignorant and expecting the other husbamds to be killed. When that doesn't happen, the truth dawns on all of them...and day 40 is a total bloodbath.
"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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Quote:
On Aug 16, 2017, LobowolfXXX wrote:
. . .

Now say there are two couples. On day 1, nothing happens, because each wife thinks the king was talking about the other wife's husband. But each wife expects that the other wife will kill her husband, for the same reason that the husband gets killed in the exam when there's one unfaithful husband.

. . .



I am not sure I follow this.

Since each wife is, herself, cheating with the other's husband, each knows that at least one cheating husband is the husband of the other wife. She still doesn't know whether her own husband is cheating, and so does not kill him. What is it that drives the conclusion that her own husband is cheating?
LobowolfXXX
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Let's say I'm wife 1. I know that at least one husband is cheating. If *my* husband were not cheating, then wife 2 would know that it's HER husband who's cheating, and she would have killed him on day 1.

When she doesn't, it's clear that Wife 2 doesn't know her husband is cheating. And that can only be because MY husband is cheating.

The same thing applies to wife 2; when wife 1 doesn't kill her husband, she knows that wife 1 can't identify the cheating husband, which means they both are.

So on the SECOND day, they both kill their husbands.
"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."
landmark
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I think I must be missing something here as well. Why doesn't the bloodbath occur on day 2 for any number of couples. Shouldn't each wife look at the results of day 1 and say--oh, nobody else has a guilty husband, it must have been mine--and then do the deed?
the Sponge
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Taking the words literally: If nobody learns their husband is a cheater, then nothing will happen. The wife won't know unless they are told. So the wives just keep their mouths shut, nobody finds out, thus nobody dies.

right?
landmark
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"If *my* husband were not cheating, then wife 2 would know that it's HER husband who's cheating, and she would have killed him on day 1. "


Why? Why would Wife 2 know that her husband is cheating? There's nothing to indicate that Wife 2 knows the true actions of Wife 1's husband either way.
the Sponge
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I'm with landmark.
With 3 or more, unless the wives tell each other, there is no way they would know their husband is cheating. They don't even know the other wives know anyone is cheating.
LobowolfXXX
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Quote:
On Aug 16, 2017, landmark wrote:
"If *my* husband were not cheating, then wife 2 would know that it's HER husband who's cheating, and she would have killed him on day 1. "


Why? Why would Wife 2 know that her husband is cheating? There's nothing to indicate that Wife 2 knows the true actions of Wife 1's husband either way.


Everyone has been told that at least one husband is cheating
"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."
landmark
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"If my husband were not cheating, then wife 2 would know..."

I still don't understand this. How does wife 2 know that? She knows one husband is cheating, but if wife 1's husband is not cheating, wife 2 does not know that husband 1 is a non-cheating husband if there are other couples.
LobowolfXXX
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In the excerpt you're quoting from, there was a hypothetical "Now let's say there are two 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."
the Sponge
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Quote:
On Aug 16, 2017, the Sponge wrote:
Taking the words literally: If nobody learns their husband is a cheater, then nothing will happen. The wife won't know unless they are told. So the wives just keep their mouths shut, nobody finds out, thus nobody dies.

right?
the Sponge
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Quote:
On Aug 16, 2017, the Sponge wrote:
I'm with landmark.
With 3 or more, unless the wives tell each other, there is no way they would know their husband is cheating. They don't even know the other wives know anyone is cheating.
0pus
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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?
landmark
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Lobo, how about this if you have some time. Let me set up the three couple situation, and maybe you can walk us through the solution.

Assume wife 1 2 3.
Wife 1 cheats with husband 3, wife 2 with husband 1, and wife 3 with husband 2.

Wife 1 thinks to herself, "If my husband is innocent, then one of the other two women did not cheat, while the other woman must have cheated with the innocent woman's husband. So, either a) wife 2 is innocent, and wife 3 slept with husband 2; or b) wife 3 is innocent and wife 2 slept with husband 3."

"But I slept with husband 3, so I know that case b is not possible. Therefore, if my husband is innocent, then wife 2 is innocent and wife 3 slept with husband 2. "

And... that's about as far as I can get. I assume at some point, wife 1 will reach a contradiction that leads her to conclude that her husband cannot be innocent.
the Sponge
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Quote:
On Aug 17, 2017, landmark wrote:

Assume wife 1 2 3.
Wife 1 cheats with husband 3, wife 2 with husband 1, and wife 3 with husband 2.


Actually, it doesn't even say they cheat with multiple women. It could be one woman, or only 20....
the Sponge
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landmark
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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).
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