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View Full Version : Husbands with Horns (Puzzle)


Paragon
10-18-2006, 09:42 AM
I think there are some subtle results to this puzzle beyond the scope of the puzzle itself. Let me know what you think. It at least has a fun story to it, and I know there are multiple versions.

Once upon a time there was a town with just husbands and wives. But, there was something magical about it. It just so happened that when a wife cheated on her husband, he would grow an ugly pair of horns out of his head. Strangely, they would be completely invisible and undetectable by the cheated husband. Luckily for the wife, it was also considered impolite for anyone to mention seeing the horns. Basically, no one ever discussed the subject, even though they were all aware of it.

However... if a husband ever was able to discover he had grown horns, he would wait until midnight of that particular day, then take his wife and leave town forever.

Anyway, each and every day in the village square, a meeting was held and everyone attended. People could clearly see who had horns and who did not during this daily ritual. One day though, a stranger from outside the town came passing through. He had something to share with the town, so he got up in front of them to say something. His words were:

"Some of you have horns"

... and with that he left the town.

Now for the problem. Assume that at least one husband has horns and that no wives cheat on their husbands after this event. Also assume these husbands are stellar logicians.

In general, what will happen, if anything? Perhaps start with a specific example. The interesting question to me is this. What did the stranger really do? What information did he provide?

If I was confusing at some parts (probably) just ask and I'll clarify.

Darryl_P
10-18-2006, 09:57 AM
I've heard this one before, but it was a much less feminist version...

Having horns seems like a sign of shame. The wife cheats then the husband gets the shame!?

Then when he finds out, he takes her with him!!???

WTF!? /images/graemlins/confused.gif

Paragon
10-18-2006, 11:15 AM
Yeah I thought for the children's sake instead of murdering the wife at midnight I'd take some poetic license /images/graemlins/smile.gif I think another version involves monks that don't speak to each other, but are getting a disease with a red spot on their face or something.

Nielsio
10-18-2006, 11:32 AM
It's quite complex because of the different ways that can be cheated; but there's probably something you can extract still.

One piece of information you have yourself as a man is whom you have slept with.

The information the visitor gives is such that he himself does not have horns, so any horns he counts is the total, and whatever the male citizens observe could be one less.

SNOWBALL
10-18-2006, 12:01 PM
I've never heard this one, but I think the answer is that everyone will leave town.
The guys with horns will become aware of it, and leave. After that, the guys without horns will become paranoid that they must have horns, since they can't see anyone else with horns.

soon2bepro
10-18-2006, 12:21 PM
He's not giving any new information. Everyone could see some people had horns.

soon2bepro
10-18-2006, 12:22 PM
Unless there's only one guy with horns, in which case he will become aware that he's the one.

Darryl_P
10-18-2006, 01:09 PM
Answer in white:

<font color="white"> If there are n guys with horns, they will all leave on the nth day, the first being the day the stranger came.

To see this, just go through the case of n=1,2,3 and notice the pattern.

If only one guy has horns, he'll see none and leave immediately.

If two guys have horns, they'll watch the one guy they see and see what he does. If he doesn't leave on the first day, he knows there must be another guy with horns and so it must be him. They both think it through the same way so they both leave on the second day.

If three guys have horns, they will know after the 2nd day that it couldn't have been two or else they would have both left on the second day. Therefore they know they have horns and all leave on the 3rd day.

Etc.

The significance of the stranger is that he established a fixed scenario by putting a stop to the cheating.
</font>

SNOWBALL
10-18-2006, 01:12 PM
[ QUOTE ]
He's not giving any new information. Everyone could see some people had horns.



[/ QUOTE ]

wrong. If you have horns, u can't see em. Right?

soon2bepro
10-18-2006, 02:01 PM
very nice, darryl

peritonlogon
10-18-2006, 08:47 PM
except that this time durration is arbitrary, the days are not significant. This only works with a notion of, shall we say, "shared units". I think this works up to 2 definitely, probalby 3 if eye contact and common understanding could be determined. But after that a moment becomes too long.

plus, do the husbands know that the wives stop cheating?