[bushindo]

Searched for this in the archive but didn't find anything.

On an remote island there lives a tribe. The tribe has a particular custom. If a wife discovers that her husband has been cheating on her, she would shave his head that very night and paint it red.

There are 9 cheating husbands on the island. The wives gossip among themselves, but they never tell any wife the status of her husband. As a result, each wife (cheated and non-cheated alike) knows the cheating status of every man except her own husband.

One Monday, a missionary arrived and went drinking in a bar with some of the tribe's men. Under the influence of alcohol, some men let it slip that there are a few cheating husbands (but didn't say which ones) on the island. Before the missionary left, he assembled the tribe and told them "There are some cheating husbands among you".

A couple of days passed and no shaved men appear in the morning. Then one day, exactly all 9 cheating men appeared with shaved and painted heads.

1) What day was it when the 9 cheating husbands appeared with the shaved heads?

2) This is more of an information theory question. Each wife already knows about the other cheating husbands. The missionary told them what they already knew. Why then did this happen?

[Guest]

Searched for this in the archive but didn't find anything.

On an remote island there lives a tribe. The tribe has a particular custom. If a wife discovers that her husband has been cheating on her, she would shave his head that very night and paint it red.

There are 9 cheating husbands on the island. The wives gossip among themselves, but they never tell any wife the status of her husband. As a result, each wife (cheated and non-cheated alike) knows the cheating status of every man except her own husband.

One Monday, a missionary arrived and went drinking in a bar with some of the tribe's men. Under the influence of alcohol, some men let it slip that there are a few cheating husbands (but didn't say which ones) on the island. Before the missionary left, he assembled the tribe and told them "There are some cheating husbands among you".

A couple of days passed and no shaved men appear in the morning. Then one day, exactly all 9 cheating men appeared with shaved and painted heads.

1) What day was it when the 9 cheating husbands appeared with the shaved heads?

2) This is more of an information theory question. Each wife already knows about the other cheating husbands. The missionary told them what they already knew. Why then did this happen?

if the women knew about the other women's husbands but no their own...then any woman who only previously new of 8 cheaters could assume their husband was the ninth.

[bushindo]

if the women knew about the other women's husbands but no their own...then any woman who only previously new of 8 cheaters could assume their husband was the ninth.

Each woman knows of the other 8 cheating husband, that' true. But the missionary said "There are some cheating husbands among you". That doesn't indicate that there would be 9.

Edited May 29, 2009 by bushindo

[Joe's Student]

An attempt, I think I'm probably overlooking something though.

I'm presuming every woman on the island is of sound body and mind, and capable of thinking logically?

1) I would say it would be the 9th morning after the announcement. Say, as an example, that there was only one cheating husband. Every wife bar the cheated wife would know who the cheater was. So then the cheated wife thinks, "Hmmm, how come I haven't been told who the cheater was?" She then realises that it must be her husband, because she didn't hear anything, and then paints and shaves his head the next morning.

Now say there were only 2 cheaters, and there wives were A and B. During the day, after the announcement, A and B, both hear of the other's cheating husband. They don't think anything more of it. No one is shaved the next morning, so both A and B realise that there must have been another cheating husband, so that A and B both heard about a cheater, and therefore didn't shave their own husband. They then realise that as they had only heard of one cheater, and the fact they had deduced there were two, that the other cheater had to be their own husband. The next morning both A and B would shave the husbands.

So it stands that if there are nine cheaters, each of the nine cheated wives hear of eight cheaters, and when no one is shaved on the 8th morning following the announcement, they all realise that there must be another cheater out there, who they don't know about i.e their own husband. So on the 9th morning all nine wives shave their husband.

[Joe's Student]

As for the second question, I'm not sure exactly what you're asking? Are you asking why a visiting missionary's statement causes the wives to act, and why they didn't before? Are you looking for a logical answer or is it more a general thought type question?

[Guest]

The wives are smart

Its a mathematical induction problem...

Lets take the case of only one cheating husband..

When told there is a cheating husband..

The cheated on woman will know immediately because, the women gossip and if there was a cheating husband and its not hers then she would know about it.

Now lets take the case of 2 cheating husbands...

If a woman who is being cheated on but does not know it is reasoning it out:

She assumes that her husband is not cheating on her.

She has been told that there is at least one cheating husband. She also has gossip about one cheating husband. Now if her assumption is right then it is a case of only one cheating husband, so the other wife will paint her husbands head that night.

If that does not happen, then she knows her husband is also cheating.

Now lets take the case of 3 cheating husbands...

Each wife who is being cheated on knows about 2 cheating husbands. If they assume that their man is not cheating, then is a case of 2 cheating husbands.. so they wait for the 2nd night, and if no one's head is painted, they all 3 of them know their man is cheating (coz their assumption has been proven wrong).

The other women on the island know about 3 cheating men, so they will go by the same logic.. but after the 3rd night, they will have their assumption (that their man is not cheating) proved right.

This case can be expanded to the case of 9 cheating men.

Ans:

1) the 9th day

2)It is the kernel of inductive reasoning (read explanation)

[Guest]

Every wife knows of 8 cheating husbands. And don't think their husband is one of them. So it will take 8 nights and no heads shaved for them all to assume their husband is a cheater, so then they shave their husbands heads on the 9th day.

[Guest]

wow... 4posts in the time it took me to type my answer

[Guest]

damn, i reread the question, work out the answer and before i can put it down there are 600 correct answers. guess i'm just slow.

[Guest]

Searched for this in the archive but didn't find anything.

On an remote island there lives a tribe. The tribe has a particular custom. If a wife discovers that her husband has been cheating on her, she would shave his head that very night and paint it red.

There are 9 cheating husbands on the island. The wives gossip among themselves, but they never tell any wife the status of her husband. As a result, each wife (cheated and non-cheated alike) knows the cheating status of every man except her own husband.

One Monday, a missionary arrived and went drinking in a bar with some of the tribe's men. Under the influence of alcohol, some men let it slip that there are a few cheating husbands (but didn't say which ones) on the island. Before the missionary left, he assembled the tribe and told them "There are some cheating husbands among you".

A couple of days passed and no shaved men appear in the morning. Then one day, exactly all 9 cheating men appeared with shaved and painted heads.

1) What day was it when the 9 cheating husbands appeared with the shaved heads?

2) This is more of an information theory question. Each wife already knows about the other cheating husbands. The missionary told them what they already knew. Why then did this happen?

http://brainden.com/forum/index.php?showtopic=28

[Guest]

Searched for this in the archive but didn't find anything.

On an remote island there lives a tribe. The tribe has a particular custom. If a wife discovers that her husband has been cheating on her, she would shave his head that very night and paint it red.

There are 9 cheating husbands on the island. The wives gossip among themselves, but they never tell any wife the status of her husband. As a result, each wife (cheated and non-cheated alike) knows the cheating status of every man except her own husband.

One Monday, a missionary arrived and went drinking in a bar with some of the tribe's men. Under the influence of alcohol, some men let it slip that there are a few cheating husbands (but didn't say which ones) on the island. Before the missionary left, he assembled the tribe and told them "There are some cheating husbands among you".

A couple of days passed and no shaved men appear in the morning. Then one day, exactly all 9 cheating men appeared with shaved and painted heads.

1) What day was it when the 9 cheating husbands appeared with the shaved heads?

2) This is more of an information theory question. Each wife already knows about the other cheating husbands. The missionary told them what they already knew. Why then did this happen?

This was posted by Rookie1ja:

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?

Sorry I don't know how to add links to posts.

[bushindo]

http://brainden.com/forum/index.php?showtopic=28

Ah, there it is. I did a search for "cheating husbands" and found nothing in the first 2 pages, so I assumed that the problem wasn't posted. Turns out I should have searched for "unfaithful wives".

Good job to joe, james, and adiace. Anyways, the second question still stands. Let me clarify the second one. Every wives already knew of some cheating husbands, so the missionary didn't tell them what they didn't know. Explain where the extra information entered the system. Adiace made a stab at the second question, but I feel it is unsatisfactory.

Edited May 29, 2009 by bushindo

[Guest]

@bushindo: I think you gave away too many clues

If ur not a fan yet, read xkcd webcomics.

And if you want the mother of all logical puzzles (well it won't be hard after you have solved this one), check out the Blue-Eyes Puzzle

[rookie1ja]

This was posted by Rookie1ja:

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?

Sorry I don't know how to add links to posts.

just paste the URL in the post - http://brainden.com/forum/index.php?showtopic=28

feel free to add better / more comprehensible explanation of answer

btw, you will see more variations of this puzzle if you search for "josephine"

[Guest]

As to the second part

He did give them some information that they did not have before. The wives did not shave heads beacuse they would assume that the cheated on wives did not know that there was a chance they were being cheated on. After his annoncement they were certain every wife knew and that there should have been some shaved heads.

[Guest]

The logic in this puzzle makes no sence. It would be just as logical to assume after the first day with no painted heads that they were being cheated on. This would appy to every wife in the tribe. Most of all, when a women finds out you have been cheating and wants to cut something off its not the hair they go for.

[HoustonHokie]

Here's what I've never understood about the gossip ring in these type of puzzles:

They gossip about the cheating nature of each individual husband, but never seem to share their thoughts on the total number of cheating husbands. So while they have useful information about what eveyone else's husband is doing, they can't even deduce what their own husband is doing until you add the extra information, which is really a start time. When you add the specific start time, each wife can count how many days it's been since the announcement and therefore they can confirm whether there are 8, 9, or 10 cheating husbands in their midst (wives of cheaters know of 8 and suspect there could be 9, wives of the faithful know of 9 and suspect there could be 10). I guess that these wives are just too sensitive to even that kind of information, although I'm sure there are ways to get it without a direct wife-to-wife confrontation. What they need - whether it's a simple poll, or a visiting missionary's announcement - is to be coordinated in their efforts to expose the unfaithful. To me, the gossip poll is more efficient, but produces a less interesting puzzle.

And here's the other thing I don't get:

What about the double standard here? Presumably the wives know of the cheating husbands because they are the ones the husbands are cheating with! It's because Sally has been cheating with Harry that she can issue the first gossip rumor about Harry - she doesn't have to expose her own guilt, but condemns him. Perhaps the husbands should get together and share what they know. A woman with a shaved head is probably much more ostracized than a man...

[Guest]

The wives are smart

Its a mathematical induction problem...

Lets take the case of only one cheating husband..

When told there is a cheating husband..

The cheated on woman will know immediately because, the women gossip and if there was a cheating husband and its not hers then she would know about it.

Now lets take the case of 2 cheating husbands...

If a woman who is being cheated on but does not know it is reasoning it out:

She assumes that her husband is not cheating on her.

She has been told that there is at least one cheating husband. She also has gossip about one cheating husband. Now if her assumption is right then it is a case of only one cheating husband, so the other wife will paint her husbands head that night.

If that does not happen, then she knows her husband is also cheating.

Now lets take the case of 3 cheating husbands...

Each wife who is being cheated on knows about 2 cheating husbands. If they assume that their man is not cheating, then is a case of 2 cheating husbands.. so they wait for the 2nd night, and if no one's head is painted, they all 3 of them know their man is cheating (coz their assumption has been proven wrong).

The other women on the island know about 3 cheating men, so they will go by the same logic.. but after the 3rd night, they will have their assumption (that their man is not cheating) proved right.

This case can be expanded to the case of 9 cheating men.

Ans:

1) the 9th day

2)It is the kernel of inductive reasoning (read explanation)

Does this answer assume that there are only 9 husbands on the island? What if there were 30 husbands and still only 9 unfaithful ones. Does this method still work?

[Guest]

oops, never mind.

[Guest]

the criteria for a husband to hav a shaved head is his wife finding out.

all wives kno that eight other husbands are cheating.

now.. if there were only two couples..

on the first day... each wife would think... if my husband did not cheat.. then the other wife would ve shaved her husbands head last night cos she knows the cheating status of my husband and that atleast one husband cheats...

she hasnt.. so she knows my husband cheats.. thus on the second day..

both husbands head would be shaven...

the case for 9 husbands or n husbands can be easily extended thru induction... thus the 9 husbands arrive head shaven on the 9th day...