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A Small Town Affair (May 2023 Challenge Question)

Posted April 30, 2023 12:00 AM
Pathfinder Tags: challenge question

There is a small, rural village in an unusual country that you have never heard about.

This community has 50 married couples, each a husband and wife. The country has an edict - wives must kill cheating husbands as soon as they have proof.

All husbands in this village are adulterous, and all wives are aware that the other 49 husbands in the village are unfaithful. Each also believes her husband to be the last honest man. (Always the last to know, right?)

One day, that country's king arrives, and reveals that at least one husband has been unfaithful to his wife. The king then leaves.

What happens next? When do the wives find out about their own husband's betrayal?

Solution, posted 5.19.23

Nothing happens for 49 days. On day 50, all the wives kill their husbands.

The king revealed that at least one husband was adulterous. Had it been only one husband, that man’s wife would know of zero cheating husband’s at the time of the reveal. Knowing that all the other wives failed to kill their own husbands, and herself knowing zero cheating husbands, she would be able to infer it was her own husband after one day.

However, Ginny knows of 49 cheating husbands. Her own husband, Perry, is honest, as far as she knows. By day 49, she is expecting her friend Clara to kill her own husband, Paul, whom Ginny knows is cheating on Clara. On day 50, Ginny discovers Paul is still alive. She can conclude that the other village wives haven’t killed their own husbands, because they know Perry has been unfaithful. (Remember, each thinks their own is the last honest man!)

Each extremely rational and logical wife, calmly eliminates their own husband with the same reasoning.

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#1

Re: A Small Town Affair (May 2023 Challenge Question)

04/30/2023 5:00 AM

I don't see how this can be resolved. You have to delve into the minds of the wives, and, there's a huge timing problem.

Even if you reduce it to two couples. Wife A must look at wife B, and think if she is not sleeping with my husband then she knows that her husband is sleeping with me, but, she hasn't killed her husband yet, so she must be sleeping with my husband and therefore I must kill him. But at this point wife B does not know if wife A killed her husband because she was innocent or because she worked it out quicker than herself. Because everyone thinks they are smarter than the next person wife B probably just assumes that wife A was innocent, and, took a long time to work out that her husband was not. "A long time" is a very subjective concept in these circumstances.

Once you get to three couples it gets much more complicated, because the adultery can take different forms. With wives in upper case and husbands in lower case.

Either A and b, B and c, C and a.

Or A and b, A and c, B and a

In both cases the wives could all be aware of the other two husbands cheating before the kings visit, and now of course "a long time" becomes unknowable.

I must therefore conclude that nothing happens after the kings visit. Or that I can't possibly work something out about a country I have never heard of.

I must be wrong so I'm looking forward to a better answer.

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#2

Re: A Small Town Affair (May 2023 Challenge Question)

04/30/2023 9:45 AM

DNA testing of the children...

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#3

Re: A Small Town Affair (May 2023 Challenge Question)

04/30/2023 10:29 AM

"What happens next? "

All husbands leave town as quickly as possible.

"The country has an edict - wives must kill cheating husbands as soon as they have proof."

"When do the wives find out about their own husband's betrayal?"

Shortly thereafter.

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#4

Re: A Small Town Affair (May 2023 Challenge Question)

04/30/2023 4:21 PM

Nothing happens....the wives have all been unfaithful...and will accept no proof against their own husbands for a crime they have committed themselves...

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#5
In reply to #4

Re: A Small Town Affair (May 2023 Challenge Question)

04/30/2023 7:51 PM

The king doesn't give the women any information they didn't already know, i.e., at least one man is a player. They all believe 49 are cheating, just not agreeing on which 49.

However, anything the king says is news and the women will start talking about it. When the first woman claims her husband is innocent and the other 49 are guilty, there will likely be a lot of disagreement.

Sometimes communication may be a bad thing. The king should stick to making war on other kingdoms, less bloodshed...

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#14
In reply to #5

Re: A Small Town Affair (May 2023 Challenge Question)

05/02/2023 6:14 AM

"The king doesn't give the women any information they didn't already know"

But they now know that every wife now knows that at least one husband is cheating.

Look at the simple case of just two couples. Before the kings visit all four of the players are cheating, but they only know about their own dalliance. After the king's visit each wife knows that if the other wife is innocent then she knows that her husband is guilty. Because each potentially innocent wife has not killed her husband instantly the other then knows that her husband is guilty, and can kill her own husband. But here's the problem: "What does instantly mean?".

If the original question was changed from:

"The country has an edict - wives must kill cheating husbands as soon as they have proof."

to:

"The country has an edict - wives must kill cheating husbands during the night after the day they have proof, and, announce their action the following day."

Then in the case of two couples the solution is easy. No one dies the first night, but on the second night both husbands are killed.

This solution is now easy to extrapolate to fifty couples.

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#6
In reply to #4

Re: A Small Town Affair (May 2023 Challenge Question)

05/01/2023 12:43 AM

I think at least 2 wives have been unfaithful. Say 49 husbands have had affairs with one woman. To be unfaithful, her own husband would have to have had an affair with a second woman. Minimum of two women, leaving 48 faithful women, right?

I doubt this helps answer the question, but it's an interesting possibility.

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#7

Re: A Small Town Affair (May 2023 Challenge Question)

05/01/2023 11:27 AM

Each of the 49 wives already knows their husbands are players..

all they need is a proof to kill their husbands..

When the king made the announcement about a husband being playful, each of the wives took the king's words as the needed proof..

So all of the 49 husbands automatically becomes a suspect and based on the king's announcement included the 50th husband, hence that night all husbands were killed by their respective wives ..

The following day the town becomes a widow's town...

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#9
In reply to #7

Re: A Small Town Affair (May 2023 Challenge Question)

05/01/2023 4:21 PM

They know the others are unfaithful, but not their own...

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#10
In reply to #9

Re: A Small Town Affair (May 2023 Challenge Question)

05/01/2023 4:31 PM

" All husbands in this village are adulterous, and all wives are aware that the other 49 husbands in the village are unfaithful"

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#11
In reply to #10

Re: A Small Town Affair (May 2023 Challenge Question)

05/01/2023 6:35 PM

other 49 husbands in the village are unfaithful. Each also believes her husband to be the last honest man. (Not unfaithful)

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#17
In reply to #11

Re: A Small Town Affair (May 2023 Challenge Question)

05/02/2023 11:01 AM

So the wives knowing all the husbands are guilty except their own, have decided to kill the husband that they happen to be cavorting with that night instead of theirs to be sure, not realizing every wives have the same plan that night...

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#22
In reply to #7

Re: A Small Town Affair (May 2023 Challenge Question)

05/19/2023 10:07 AM

This is the right answer.

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#23
In reply to #22

Re: A Small Town Affair (May 2023 Challenge Question)

05/21/2023 4:58 AM

Huh? According to who?

I already showed in post 1 and post 14 that if we make the necessary change to the question, then with only two couples it take 'til the second night before the cull happens.

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#8

Re: A Small Town Affair (May 2023 Challenge Question)

05/01/2023 4:19 PM

The King, in revealing the one husband, we must assume that the name of one of the husbands is revealed, otherwise nothing is new, correct? This is not clear in the question...

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#15
In reply to #8

Re: A Small Town Affair (May 2023 Challenge Question)

05/02/2023 6:19 AM

"otherwise nothing is new, correct?"

See my reply #14

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#12

Re: A Small Town Affair (May 2023 Challenge Question)

05/01/2023 10:57 PM

All the men die the second night.

When all the women wake up the next morning and see all the husbands alive, they now have to believe their husband is the guilty party. The next night.....

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#13
In reply to #12

Re: A Small Town Affair (May 2023 Challenge Question)

05/02/2023 12:46 AM

If the King revealed the name of one of the unfaithful husbands, not clear but perhaps implied in the question, then his wife would have killed him, and there would be one dead husband. Then the wife would tell all the other wives that their husbands had to have been unfaithful, since she knew they were all unfaithful except for her husband, until proven wrong by the King...

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#16

Re: A Small Town Affair (May 2023 Challenge Question)

05/02/2023 10:25 AM

I think they track down the King and kill him. And then after a respite, some soul searching, and a couple of confrontations, adopt the new name of "Swingerville" for their little town.

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#18

Re: A Small Town Affair (May 2023 Challenge Question)

05/04/2023 7:46 AM

Do they form a Republic instead?

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#19

Re: A Small Town Affair (May 2023 Challenge Question)

05/04/2023 10:48 PM

Nothing happens. The king's words do not provide proof of who is adulterous so no wife is compelled to kill their husband.

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#20

Re: A Small Town Affair (May 2023 Challenge Question)

05/19/2023 7:36 AM

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#21

Re: A Small Town Affair (May 2023 Challenge Question)

05/19/2023 9:30 AM

When the king gets back to his castle, the queen kills him. Her successful defense in court comes from her claim that she was compelled by law to kill the self-admittedly adulterous king. A short time after becoming sovereign, the queen rescinds the "cheating husband" law.

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#24

Re: A Small Town Affair (May 2023 Challenge Question)

07/11/2023 9:34 AM

The only way this could have happened......is if the men were sleeping with other men, not women. Otherwise the women were cheating too. A modern society. And a modern outcome.

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