Brain teaser thread

[CyberGnu]

John, too easy.

40 days after the mayors speech, every unfaithful woman is shot by her husband.

[CyberGnu]

The trick is to reduce the problem to one wife, then two etc etc.

If there was only one unfaithful woman in town, everyone would know who it was except her husband. That poor guy would know that all other women are faithful, therefore when the mayor says there is one unfaithful woman, it has to be his wife. He would thus shoot her.

If there were two unfaithful women in town, everyone would know except their husbands, who thinks there are only one woman. After the mayors speech, he expects that the other husband would realize his wife is unfaithful, and kill her at midnight.

When he wakes up in the morning and sees that no woman has been killed, he must draw the conclusion that the other guy knows of another unfaithful woman, which must be his own wife.

The other guy reasons the exact same way, so the second night both wifes are shot.

If there are three wifes, it would take three nights before the three husbands realize that the two women they know of aren;t dead yet.

After a lot of counting, and possibly tying all wifes to lamposts to keep them from running from a certain death, the 40 husbands realize that there must be one more than the 39 wifes they know of, and erupt in an orgy of violence.

Good times.

[Tuberski]

Originally posted by JohnM2433
Nope, no one got the answer to mine yet. It's strangely paradoxical, yet in a strange way, it makes perfect logical sense. I think. It's not at all obvious. If no one can figure it out, I'll give the answer if you all give up.

Hint: Think recursively. Or rather, assume that the men in the problem will.

It's easy, June 1st isn't a summer day. !st day of summer is June 21, I believe.

[Urban Ranger]

No, that's the first day of Autumn

[CyberGnu]

So, here is a new one:

What comes next in this serie?
PN BP KT RK ??

[CyberGnu]

In sweden summer is between June 1'st and September 1'st, btw

[Urban Ranger]

Cyber,

There is a problem with your reasoning.

First, there are 40 unfaithful wives in town, so the husbands of these 40 wives know that there are 39, other men know there are 40.

Second, when the Mayor speaks of an unfaithful woman, it has to be his own wife. So, per the custom, he kills her that night.

Third, the next day, the husbands of the 39 remaining wives think there are 38 unfaithful wives. The rest of the men, including the Mayor, know that there are 39.

Then what?

[CyberGnu]

Urban, didn't see the logical flaw that the Mayor can;t speak of anyone's elses wife but his own... Hmmm... I think that ruins the entire problem...

Without the induction of the unknown, the problem isn't solvable. Instead assume that it is one of the wives who has found out, and the probelm works

[Capt Dizle]

Small Town Affair: The Mayor would not lie because it is not logical. The Mayor has not discovered that his wife is unfaithful or he would just shoot her. The Mayor has not broken the taboo because he did not speak to a specific man about a specific wife.

Each man being logical decides to use a logical means to find out if his wife is faithful. He asks other men how many unfaithful wives are in the town. The other men do the same. The answers are all ither 40 or 39. Soon it becomes apparent that the 40 men who answered 39 have unfaithful wives. So, at midnight on June the second the 40 unfaithful wives are shot.

[JohnM2433]

Yup, CyberGnu has the "correct" answer, but Urban Ranger and jimmytrick raise a good point: If one man can speak generally to another about a woman who might or might not be the latter's wife, then a man could find out the true number of unfaithful wives by asking a man whose wife he knows is faithful. If not, then the mayor would not be able to deliver his message.

But the mayor is not telling the men anything they do not already know! Each man obviously knows that there is at least one unfaithful wife in the town. That's what makes the answer seem so paradoxical to me, since at first it seems that no new information is revealed. What actually does change is what each man knows about what each man knows about what each man knows... etc.

If a man answered another man's question about how many unfaithful wives there were, he effectively would be telling the latter whether his wife was unfaithful, so one could imagine that this would be covered by the taboo. But the mayor is not directly revealing anything that is not already known, and in fact only pointing out some common knowledge, so his message is not taboo. However, because all of the men now know that they all know that they all know... ect., they are able to deduce their own wives' faithfulness or unfaithfulness, despite not being directly told anything new.

Dirty.

And while it might seem horrific for all of those men to shoot their wives, bear in mind that if they hadn't, every other man in town would have shot his wife on the following night!

[CyberGnu]

Hey, why is 'correct' in citation marks?

[Urban Ranger]

Originally posted by JohnM2433
Yup, CyberGnu has the "correct" answer, but Urban Ranger and jimmytrick raise a good point: If one man can speak generally to another about a woman who might or might not be the latter's wife, then a man could find out the true number of unfaithful wives by asking a man whose wife he knows is faithful. If not, then the mayor would not be able to deliver his message.

A couple of flaws I see this problem has:

1. Since everybody else other than the Mayor knows the Mayor's wife is unfaithful, announcing this fact merely says the Mayor finds this out somehow. Why would anybody else expect his own wife is also unfaithful?

2. When a man in this town asks another man whose wife this first man know is faithful how may unfaithful wives there are in town, I expect the answer really depends on whether the wife of this first man is faithful or not. So no deduction can be made indirectly.

[JohnM2433]

Originally posted by CyberGnu
Hey, why is 'correct' in citation marks?

Because the problem is somewhat ambiguous, as Urban Ranger's and jimmytrick's comments indicate. It probably could have been worded better, to make more explicit the precise meaning. But the answer you gave is the one I've seen before, and probably what the person who put the problem together was looking for. That's why I called it the "correct" one.

Urban Ranger:

1. The mayor need not be talking about his own wife, depending on what interpretation we give the rules, as discussed above.

2. I'm suggesting that because the answer depends on whether the wife of this first man is faithful or not, the second man is not allowed to answer the question.

[CyberGnu]

Well then

No takers for my problem?

Complete this series:
PN BP KT RK ??

[JohnM2433]

Beats me. I was never any good at letter series. Someone'll probably get it, though. Maybe they're just still working on it.