Every man in a village of 100 married couples has cheated on his wife. Every wife in the village instantly knows when a man other than her husband has cheated, but does not know when her own husband has. The village has a law that does not allow for adultery. Any wife who can prove that her husband is unfaithful must kill him that very day. The women of the village would never disobey this law. One day, the queen of the village visits and announces that at least one husband has been unfaithful. What happens?
Every man in a village of 100 married couples has cheated on his wife...
- Thread starter CygnusX
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It depends. If the queen knows who it was, then all men are executed(1 gets killed+others on revenge), if she doesn't then it was the king(if there is a king, and the queen is subject to the same laws)...
Ok, there are a couple of options here.
1) If the women discuss it then they will realise that all of the husbands have been cheating (everyone knows that 99 other husbands have) and they all have to die.
2)They don't discuss it. In this case nothing has changed, they all new that other husbands were cheating anyway, the queen told them nothing new.
1) If the women discuss it then they will realise that all of the husbands have been cheating (everyone knows that 99 other husbands have) and they all have to die.
2)They don't discuss it. In this case nothing has changed, they all new that other husbands were cheating anyway, the queen told them nothing new.
Nothing that hasn't already happened before the announcement. If every woman instantly knows when a man other than her husband has cheated, the queen's announcement doesn't contain any information that they don't know already.
Therefore the state of the village remains unchanged. The husbands could already all be dead, or alive, but that is irrelevant for the purpose of this question.
EDIT - I think this is the original problem, which has more information:
A certain village contains a number of married couples, of which k husbands are cheating on their wives. Every woman is aware of all the cheating taking place, expect for the infidelities of her own husband. In order to uphold a strict morality, the women of the village make a pact: any woman who learns that her husband has been cheating will kill him that night and dump his body in the town square for all to see. However, because no one wants to tell another woman that her husband is being unfaithful, this information is never communicated, and so, the cheating continues. Some time later, at a town meeting, the chief announces, "I want the cheating in this village to stop." Then, k-1 nights pass uneventfully, but on the kth night, all k cheating husband are killed by their wives. How did this happen?
Therefore the state of the village remains unchanged. The husbands could already all be dead, or alive, but that is irrelevant for the purpose of this question.
EDIT - I think this is the original problem, which has more information:
A certain village contains a number of married couples, of which k husbands are cheating on their wives. Every woman is aware of all the cheating taking place, expect for the infidelities of her own husband. In order to uphold a strict morality, the women of the village make a pact: any woman who learns that her husband has been cheating will kill him that night and dump his body in the town square for all to see. However, because no one wants to tell another woman that her husband is being unfaithful, this information is never communicated, and so, the cheating continues. Some time later, at a town meeting, the chief announces, "I want the cheating in this village to stop." Then, k-1 nights pass uneventfully, but on the kth night, all k cheating husband are killed by their wives. How did this happen?
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This question makes a lot more sense.
If there was only 1 cheating husband then his wife would know it was him after the first night because her magic cheating sense wasn't aware of any other infidelities (and the chief confirmed that there has been cheating).
If there were 2 cheaters, one of the cheated wives (wife A) would be aware of exactly one cheater (husband B) and, noticing that B's corpse wasn't present in the square after the first night, she would deduce that wife B was aware of another cheater, husband A (otherwise, as in the first example, wife B would have killed him). Wife A therefore deduces that her husband must be the other cheater and she'll have to kill him the next night.
Keep iterating as above for k cheaters.
The solution works because the chief effectively pushed the reset button and allowed the women to combine their knowledge of the number of cheaters with the number of days passed since the announcement with no killings. Without one of those two bits of information the women could not know if their own husbands had cheated.
the village is in San Francisco, so there is only 1 marriage made up of a man and a woman, the rest are all women/women.
Nobody has stated the obvious:
Nothing happens, because adultery is illegal and those men were cheating on their wives with someone else's wife. Therefore all of the women are guilty of cheating as well.
The reason the question is asked is not for mathematical reasons, but simply to deduce the preconceived prejudices in the interviewee. Everyone assumes a man is unfaithful, but never looks to the women that they are being unfaithful with.
Nothing happens, because adultery is illegal and those men were cheating on their wives with someone else's wife. Therefore all of the women are guilty of cheating as well.
The reason the question is asked is not for mathematical reasons, but simply to deduce the preconceived prejudices in the interviewee. Everyone assumes a man is unfaithful, but never looks to the women that they are being unfaithful with.
The question never stated that the cheating took place with a woman either.
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