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# Josephine

## 42 posts in this topic

Unfaithful Wives - Back to the Cool Math Games

An anthropologist studying a primitive tribe in a remote location in the Amazon basin, had uncovered a strange tribal custom. Whereby, if a husband found out his wife was unfaithful to him, he must execute her in a public ceremony in front of the whole tribe on the same day at midnight. It so happened that every man in the tribe knew about every cheating wife except his own, since telling a man about his cheating wife was against the tribal honor code. On the day of his departure, the anthropologist held a tribal meeting and made the announcement: “I know there are unfaithful wives in this tribe.” On the ninth day thereafter all cheating wives were executed at the same time.

How many unfaithful wives were there?

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Josephine - solution

The two questions for scroll #1 were:

1. How many husbands were shot on that fateful night?

2. Why is Queen Henrietta I revered in Mamajorca?

If there are n unfaithful husbands (UHs), every wife of an UH knows of n-1 UH's while every wife of a faithful husband knows of n UHs. [this because everyone has perfect information about everything except the fidelity of their own husband]. Now we do a simple induction: Assume that there is only one UH. Then all the wives but one know that there is just one UH, but the wife of the UH thinks that everyone is faithful. Upon hearing that "there is at least one UH", the wife realizes that the only husband it can be is her own, and so shoots him. Now, imagine that there are just two UH's. Each wife of an UH assumes that the situation is "only one UH in town" and so waits to hear the other wife (she knows who it is, of course) shoot her husband on the first night. When no one is shot, that can only be because her OWN husband was a second UH. The wife of the second UH makes the same deduction when no shot is fired the first night (she was waiting, and expecting the other to shoot, too). So they both figure it out after the first night, and shoot their husbands the second night. It is easy to tidy up the induction to show that the n UHs will all be shot just on the n'th midnight.

The recent expedition to the lost city of Atlantis discovered scrolls attributed to the great poet, scholar, philosopher Josephine. They number eight in all, and here is the first.

The kingdom of Mamajorca, was ruled by queen Henrietta I. In Mamajorca women have to pass an extensive logic exam before they are allowed to get married. Queens do not have to take this exam. All the women in Mamajorca are loyal to their queen and do whatever she tells them to. The queens of Mamajorca are truthful. All shots fired in Mamajorca can be heard in every house. All above facts are known to be common knowledge.

Henrietta was worried about the infidelity of the married men in Mamajorca. She summoned all the wives to the town square, and made the following announcement. "There is at least one unfaithful husband in Mamajorca. All wives know which husbands are unfaithful, but have no knowledge about the fidelity of their own husband. You are forbidden to discuss your husband's faithfulness with any other woman. If you discover that your husband is unfaithful, you must shoot him at precisely midnight of the day you find that out."

Thirty-nine silent nights followed the queen's announcement. On the fortieth night, shots were heard. Queen Henrietta I is revered in Mamajorcan history.

Edit (implied questions moved from solution to the wording of the puzzle):

The two questions for scroll #1 were:

1. How many husbands were shot on that fateful night?

2. Why is Queen Henrietta I revered in Mamajorca?

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OK I'll Bite!

Why was Queen Henrietta Revered?

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The night the 40 men died, she successfully wiped out the future of Mamajorcan population

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I think they should be able to figure out how many unfaithful men there are.

They can just ask eachother how many unfaithful men the other woman knows. If they ever get an answer that higher than their number then their husband is a cheater!

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Okay, the women in this kingdom are cheaters and good at maths

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okay i will. gimme a sec

okay u edited ur post so iguess u dont want it explained any more?

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why was the queen revered

thats why

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There is one possible weakness in this solution, which you may want to address in an edit or a future post.

If any husband was faithful on the day of the proclamation, but became unfaithful during the first 40 days, wouldn't that throw the logic out of order in such a way as to be impossible to tell the exact number?

Just curious since I haven't actually thought it through and I'm too tired to figure the long term effects.

Little help?

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She did not eliminate infidelity. The husbands had to cheat with someone. There are still some unfaithful women out there.

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She did not eliminate infidelity. The husbands had to cheat with someone. There are still some unfaithful women out there.

Who said the husbands didn't cheat with single women?

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I agree that this would only be a temporary solution, regardless of who the men were cheating with. While some men are unfaithful from the beginning of the relationship, many more actually become unfaithful later for various reasons. They may become bored with the current relationship or be tempted by another woman. So, the queen succeeded in taking out the current 39 cheaters, but more will be introduced. In order to keep the unfaithful husbands in check, the women would need to restart the "hunt" anytime any of them learned of an unfaithful husband. Of course, they might also want to consider taking out the women who are cheating with these men as well, since they are very likely to select other men when theirs are eliminated.

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we're talking about goddamn genocide here. lol

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The men were cheating because the only punishment they expected to receive was to be left by the woman they didn't want to be with anyway.

Now they fear DEATH! That, I would seriously think, would eliminate cheating. There would just be more divorce. Much easier than dying!

definitely!

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Did anyone else realize there was no question posed? That was story. A strange one, but a story nonetheless, not a riddle.

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i reckon they must have all cheated on the extensive logic exam if NONE of them had already realised their husbands were cheating on them

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I agree this could be a flawed riddle.

Each woman could ask one or more other women simply how many unfaithful husbands they know of. The instant any other woman says a number one higher than the number she personally knows, then she immediately knows her own husband is unfaithful. She has not directly asked at all about her own husband this way. This could be determined on the very first day, and the entire situation resolved by *everyone* at midnight.

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This riddle doesn't include any question! The tale is nice, but what's the problem?

The only thing I can do is guess that you want to hear what the tale means:

Here goes:

There were exactly 40 married couples in Mamajorca. Each night since the proclamation, every man slept with another woman than his own, and with another than any of the nights before. On the 40th night, they all came home to sleep with their own wives and were exterminated, thereby dooming the future of Mamajorca, because there would be no more offspring!

BoilingOil

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This riddle doesn't include any question! The tale is nice, but what's the problem?

The only thing I can do is guess that you want to hear what the tale means:

Here goes:

There were exactly 40 married couples in Mamajorca. Each night since the proclamation, every man slept with another woman than his own, and with another than any of the nights before. On the 40th night, they all came home to sleep with their own wives and were exterminated, thereby dooming the future of Mamajorca, because there would be no more offspring!

BoilingOil

OK ... I guess I have to amend my attitude ... so I will assume that users of my forum can not always find implied questions and they have to be led like little children ... I have moved the questions to the wording of the puzzle

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OK ... I guess I have to amend my attitude ... so I will assume that users of my forum can not always find implied questions and they have to be led like little children ... I have moved the questions to the wording of the puzzle

It's not as bad as you make it sound now... "BoilingOil" is not "users of your forum". He's only ONE idiot who sometimes doesn't even see the OBVIOUS

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here is how I see it:

let's suppose there were five cheeting husbands

Wife no5 knows that there are 4 hsbands who cheat and she thinks that Wife no4 only knows about 3 and that she thinks Wife no3 only know about 2... but it's a nonsense to think that any wife in town would believe there are only 2 or 3 unfaithful husbands when in fact there are 5 and all the wives whose husbands cheat on them believe there are 4. So I don't think you can tidy up the induction to 40.

So I think the solution of the puzzle is that every wife asked other wives how many unfathful husbands did they know and if the number was higher than the number they knew, it would mean that their husbands are cheaters too.

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one guy was shot. he was sleaping with a lot of the women and all of them found out the same time then shot him. the queen found out it was her husband.

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Hmm.

Well, I have to admit that I kind of hunched there was a more "logical" answer, but I stuck to mine :-). (in case ur wondering if the other men would give their friend away so easily, well, I guess they will with a gun pointing to their head :-))