Infedelity

[cha]

The answer is seven. We know it is not zero. If it were one, then all the women except one would know. Therefore, the only woman who knew of no cheating men would know it was her husband, and would kill him the first night. If on the second morning no man had been killed, everyone would know there must be at least two cheatng men. If there were exactly two cheating men, the two women who only knew about one man each would know it was their husbands and kill them. This goes on until the seventh day, with no deaths. By now, there are seven women who only know about six cheating men, and they kill their husbands that night. On the eighth morning, there are seven dead men.

[Coyote]

What fascinates me about this puzzle is the apparent paradox involved in it. All the wives in the village already know that some men in the village are cheating. It seems the fortune-tellers remark adds no new information, yet it's not till the remark is made that the cheating husbands are suddenly in fear for their lives.
Why should this be?

[ewan]

its a common knowledge puzzle, like the three prisoners with dots on thier backs or the muddy childern. although eveiryone in the village knows that there is some cheating going on they dont know that everyone else knows that there is no cheating going on untill the fourture teller tells them.

for example: say there is only one cheating husband, everyone except his wife knows that he is cheating. But his wife assumes that no-one in the village cheats. when she is told that at least one man is cheating it implies that it is her husband.

in the case of two both the cheated wives assume that there is only one cheating husband but when no-one is killed on the first night, they know that the wife of the cheating husband that they know about must know about a cheating husband(CH) that they dont know about... which means......! etc etc

(for those who havent seen them the prisoner puzzle is: there are three prisoners awaiting execution. the jailer takes pity on them and says 'I have 5 dots two black and three white, i will place a dot on each of your backs. If you have a white dot and can tell me that you have a white dot, then you will go free!. Being a kindly man the jailer puts a white dot on eahc of the men. The prisoners look at each others back (they are not allowed to talk) and then one ( the cleverest) of them says I have a white dot and gets to go free, how did he know?

the muddy childern puzzle if I remeber correctly is, you have a group of childern some of which have muddy faces, they come into the house and a parent says 'some of you have muddy faces! go clean them, the rest of you come and have lunch." after proccesing this information in a logical non childlike way the childern neatly divide up into those that have muddy faces and those that dont (again without talking))

[ewan]

by common knowledge i mean 'common knowledge' as in the knowledge that everyone in the group knows, rather than the answer to this puzzle is common knowledge, since I suspect that most people wounldnt be able to solve these puzzles

[HyToFry]

Good job Cha and Ewan, hell, even I understood that.



Remember, the puzzle never says that the gossip began after the fortune teller told them, the woman might have known that there were 6 men in the town cheating, and when noone died on the 6'th night, they knew that their husbands must be cheating too..

I hope I got that right.

My question, who were these men cheating with? The Town Hussy? or are there 7 woman cheating on their husbands, if so, then the casket maker might have had to make as many as 14 coffins, for the wives that were cheating. But as everyone know, it was the women, and not the men that gossiped.

[Ghost Post]

the answer is seven (I first heard this puzzle about twenty years ago: there were forty women killed in arabia the fortieth night)
The amazing thing is that we are supposing that women talks of every thing, but they don't chat about the number of untrue husband! It is for this reason that they have to wait for someone external, who starts (or initialize) the count of the meaningful days.
In fact every one knows that the correct number is six or seven, but all they need is a starting point.
-

[HyToFry]

If i lived in that town (and was for some reason cheating) I would ask my wife, "how many men are cheating on their husbands?"

If on the night of the number she said, noone died, I would get out of Dodge.

[Wonko the Sane]

I can go a solid week with no sleep if pressed, maybe I could just wait it out

[OOppsy7]

"how many men are cheating on their husbands?"???
MEN CHEAT ON THEIR HUSBANDS? you should retake grammer class HyToFry...

[Aarondalf]

Its not a bad grammar mistake, he just said husbands instead of wives, no big deal.

[HyToFry]

HAHAHAHAHAHAHAHAHAHHAHAHA

Sorry, I am a doof.. hehe

My wife would have said, none you doof.

[ewan]

what happens if the 6th wife forgives her husband, but dosnt tell anybody that she knows he is cheating becuase she is too embarresed....................... o-oh

[ewan]

hang on no it only works if all 7 forgive thie husbands onthe 7th night. A better situation is if there is only one cheating man, but he is forgiven.

[HyToFry]

hehe i like that, but the puzzles on the GL are exact it never says that sometimes a wife forgives her husband.

A better question is, what happens if one of the seven wives has only heard about 5 other men? her hubby is toast on night six, and this would confuse the hell out of everyone.... but once again exact

[Ghost Post]

Hang on. There's something wrong with Ewan's "common knowledge" explanation of why it takes the fortune teller to get things started. We know that there are seven unfaithful men. So all the women in the village know the names of at least six unfaithful husbands. Let's consider the wives with unfaithful husbands. They can reason as follows. "Suppose my husband is faithful. Then there are six women in town who only know the names of five unfaithful husbands. But it is not possible for any woman to know fewer than five names. Therefore, I know that everyone woman in town knows that there are unfaithful husbands."

Common knowledge already exists in the village. So how do the woman get started? I agree that if they
all follow the same line of reasoning starting at the same time that every cheating husband gets his on the appropriate night. I'm just not convinced that the puzzle as stated gets us on the first step of the induction ladder.

[HyToFry]

Once the fortune teller says "THere is at least one" lets speak hypothetically, and say there was only one. He would be dead that night, as his wife didn't know anyone was cheating. if there was two, then two woman would expect the other to kill her husband the first night, when the other didn't then the woman knew thier husbands were cheating, because they knew of only one, and since he didn't die the first night, they now know there must be two, and there hubby is one of them.

anyways, it works that way for any number of men. when the night arives that a woman of a cheater knows that many men are cheating, (6 men, 6'th night) and noone dies, she knows her hubby is cheating, and AXE's him.


HAHAHAHA I still like the idea of the forgiving wife, what if there was only one woman whos hubby was cheating, and she forgave him. HAHAHAH the next night EVERYONE gets it; except the guy that was cheating.

[daniel801]

i think we're all assuming each "affair" is between uniques males and females. would it change anything if it were say 2 men who have cheated with several women or if it's 2 men cheating yuk

[Tom]

"yuk"?

That's a little rude to a lot of people, isn't it?

[HyToFry]

I don't think daniel meant to be rude hehe.
yuk was rude thought, just because you can't understand it doesn't mean its yuk

Take this for example, I'm a man, and I like woman, if I was a woman, would I like men.. hmm.. I dunno. I would probably be a lesbian, or a straight woman that says, "If I was a man I would be gay"

HEHE there's food for thought.

[Ghost Post]

I understand how the reasoning works. I'm trying to argue that Coyote's question about how does the fortune teller's pronouncement make any difference. Before the fortune teller speaks everyone already knows that everyone knows that there is infidelity in the town.

The other versions of this puzzle that I have heard have a ruler proclaim that starting on a certain date the women are to kill their husbands on the night they are absolutely sure that they (the husbands) are cheating. In that case, there's no problem. The argument proceeds as outlined. In this case, however, there is just a fortune teller saying something that everyone already knew, i.e. that there was at least one unfaithful husband. And, as I have argued everyone knew that everyone else knew, so Ewan's response about common knowledge does not work in the puzzle as stated. There is nothing in the problem as stated that really starts the women reasoning and the problem only works if all the women follow the same chain of reasoning and know that the others are as well.



------------------
"I hate relativism more than I hate anything else, excepting, maybe, fiberglass powerboats."
Jerry Fodor

[HyToFry]

Okay, I see where your going.. hehe sorry.

The reason for it is that, before the fortune teller says, at leaste one man is cheating the seven woman are thinking. "I know of six men that are cheating, but none of them are my husband, so what the hell do I care" after he says it they are thinking "well, six nights from now six men will be dead" and on the seventh morn when noone was dead they knew there was one more, man that the other six woman knew about, that was they're husband.

It's not that the fortune teller told them something they didn't know, he just gave them a reason to care.

[Quailman]

Right. The chain of reasoning is such that if there is only one cheater, then one wife thinks no one is cheating, and when she learns that at least 1 is, she might not wait until nightfall. If 2 women each thought only one was cheating, they might have considered themselves part of the larger group in the prior example, but when noone is killed the first night, they catch on. This proceeds until the actual situation, where the seven wives who knew that there were six cheaters suddenly realize that they are among the cheated-on, because if there were any who knew of 5 cheaters, they would have killed their husbands the sixth day.

All the women in the town know either the actual number of cheaters or they know of one less than the total. What keeps them from killing their husbands is that they always consider themselves among the fully informed group. When the fortune-teller comes to town, they are able to follow the chain to its fateful conclusion.

[Top Gun]

In answer to HyToFry's method of finding out the best day to skip town... He could stay a lot longer than that.

Rumours may be spread by heresay (by which I assume the Minotaur means hearsay, not heresy). So all you need to do is start a fresh rumour each day.

HyToFry says to his wife "I have just heard that Wonko (to use an example) is having an affair". The rumour will spread within hours to all woman except Wonko's wife, and you're safe for another day.

Of course, eventually the town will run out of suspect men. At which time the women are either going to decide not to believe rumours (in which case you are safe) or there is going to be an extreme lack of men in the village.

[Alfie]

So let me just spell this out:
Night 0: Fortune Teller eliminates the possibility of 0 faithful men.
Night 1: The posibility of 1 faithful man is eliminated.
Night 2: 2 is gone.
Night 3: 3 is gone.
...
Night 6: 6 is gone.
So on Night 7, we know that more that 6 men are unfaithful, because no one is dead. For all that we know, 12 men could be unfaithful. In that case, on night seven, no one dies because the wives know of 11 CHs and the possibility of 11 has not been ruled out. In fact, the night on which all the men die will be the night on the number of them, so if there are seven CHs then they will die on night seven. However the puzzle does not say that any men died:

quote:

---

Then, on the eigth morning after the fortune teller came, the coffin maker received his orders. How many men were dead?

---

It does not say that the coffin maker's orders were to make coffins. For all we know, it was his turn to do guard duty for the town and those were his orders. So the answer is either zero or seven, but we don't know which one.

[Ghost Post]

Ah, you innocent fools.

How do you know the fortune teller is telling the truth? Let's presume his/her second profession is politician. Would you then still believe everything he/she says?

[ewan]

Burning: there is nothing wrong with my coimmon knowledge explaination!!!!!!!! let me try to explain it agian, i will use the example of two CHs since this is simpler

so. lets say that there are 100 married women in the village. 98 of them know of 2 CHs 2 of them know of only 1 CH. everyone knows that there are 'one or more CHs in the village'

HOWEVER the two Cheated Wives(CWs) assume that there is only 1 CH in the village and hence the other CW knows of no CHs.

if one of the CW (call her CW#2) asks the other (CW#1)'how many CHs do you know of?' the other CW will answer 'why? i dont know of any CHs!' of course this is a lie, she knows about the questioner's CH

NOW, once the fortune teller has told everyone that there are one or more CW in the village, CW#2 _knows that CW#1 is now aware of the fact that there is a cheating husband in town_, CW#2 expects cw#1 to killer her husband that night, but as we all know cw#1 fails to do this hence she must have been lieing, why would she lie? HUSBAND!!!! get in here NOW!!

so: the 'common knowledge' is not 'there is one or more CHs in the village' but 'all the other wives know that there is one or more CHs in the village'

maybey i can say that more clearly

everyone knows that everyone knows that there is one or more cheating husbands in town

[Eamonn Magrath]

I agree that the answer is only seven if that were the number of married couples in the village. If more the answer is zero.

The puzzle begs a few questions :

... Why a Fortune Teller? They generally are known for their FUTURE prophesies ... not of speaking of past deeds.

... I assume that 'unfaithful' does not necessarily mean with any of the village wives?

... The coffin maker must not be a married man! Perhaps a liberated, cheating woman!

[HyToFry]

... Why a Fortune Teller? They generally are known for their FUTURE prophesies ... not of speaking of past deeds.

Not in the land of "Matrimony", they tell only of Cheating husbands.

... I assume that 'unfaithful' does not necessarily mean with any of the village wives?

Why does this matter?

... The coffin maker must not be a married man! Perhaps a liberated, cheating woman!

Why again? they coffin maker doesn't even have to live in the town. PLUS for all we know coffin maker's wife is dead.

also, saying that the coffin maker's orders could have been everything is a PICKY, but valid point; although not in the way you see it.

When will the wives know that they are going to kill their husbands? on the MORNING of the day that they will kill thier husbands. SOO, if I knew I was gonna kill my husband, I would place the order the second I found out. See where I'm going. Now even if the coffin maker is a CH, his wife could place the order (eight coffins) and he would make them, be killed that night, and the town would just have to hope that noone else died, EVER. To be a coffin maker in most states, you have to be a licensed mortition, but i'm not sure about the land of Matrimony.


Anyways, its concieveable, although doubtfull, that eight men were killed that night, after their coffins were made

[HyToFry]

Wow, the more I think about this, the more likely it is

The mayor.. or whatever.. being the brilliant man he is, would know that, on the eighth night, eight men would be dead, so he would tell the coffin maker "make eight coffins for tomorow"

Of coarse if the Coffin maker was a CH, he would probably make 0 or 7 coffins, and get the hell out of town

[Eamonn Magrath]

If a village wife is involved it will be she who first gossips to the other wives ... think about it! ( gives same result eventually but complicates things)

By the way, the coffin maker is stated to be a he.

Why though are we told that'almost every husband' is completely faithful? If 7 unfaithful husbands is correct and if 1% is acceptable as 'almost none' then the village would have a population of some 2100 assuming a minimum of 1 child per household and no unmarried adults! This would be a small town where I come from! Are we being misled?

[daniel801]

If I were a CH, then I would start a rumor for my wife to spread that another (innocent) husband was being unfaithful and then what would happen:
the days would just tick on and on until day x (x=population of husbands) and everyone would have to rethink the deal -or- kill every man, but i don't think they'd want to do that

[HyToFry]

two things daniel, one, the riddle says the wifes.. not the men gossip, but thats just me being picky and two, this wouldn't change anything, unless you started a new rumor every day, and i'm sure that the woman would catch on, then the executions would only be put off one day, then the inocent would die

[Top Gun]

Hey !!! How come when I made the point about starting your own rumours to stay ahead of the posse it was ignored, but daniel got an immediate response ???

Anyway, HyToFry, in response to your points.

Yes you are being picky, you are not spreading gossip you're saving your skin. Also what do you call asking your wife how many unfaithful men she knows about if it is not gossipping.

On your second point; it is very hard to tell whether the women will catch on. We are dealing here with women who on the one hand can calculate upon which night they can be sure that their husband is guilty (and be confident that ALL other women are performing the same calculations without error "Opps! I lost count - maybe my husband was innocent after all") but on the other hand are prepared to kill their husband simply on hearsay and gossip.

If your wife doesn't tell the other women where she got her information, they may well not catch on.


Another interesting point is your wifes response. If we assume 7 unfaithful men (though the more I think about it, the more I like the argument for 8), and one of them is you, then when you start the rumours about the different men you may get one of three responses:

1. Most times she will rush off to spread the rumour.

2. up to 6 times she may roll her eyes and say "of course, us women have known that for ages"

3. 1 or more of those times she may blush and try to change the subject. If so, maybe you should be killing her.

[HyToFry]

HAAHAHAHA thats funny.

The best scenerio, (to me) is the forgiving wife ones, and then EVERYONE but the CH's, and wives of coarse, GET IT.

[Soma^3]

What's scary is if the fortune teller is wrong, and there's no cheating going on in the town, then the wives will wake up the next morning to find ALL the husbands are dead. Yikes!

[Evil Empire]

IF I was a cheating Husband I would have no choice but to kill my wife. Hey, it'is either her or me, plus I got a little something on the side.

[Ghost Post]

Ewan: My point is that your response only works if there are only one or two women who are being cheated on. In the problem as it is stated, every woman either knows the name of six or seven women who are being cheated on. And since the rumor mill guarantees that everyone knows the names of all other wives with unfaithful husbands, even the women who are being cheated on know the names of six women who they know know the names of at least five women who are being cheated on. If enough husbands are cheating (i.e. more than two) everyone knows that everyone knows that cheating is going on.

[Coyote]

|WARNING! THIS MAY BE THE MOST ANNOYING MESSAGE I'VE EVER POSTED!|

Actually I already knew the fortune-teller added new information (that's why I said apparent paradox). I was just hoping someone could come up with a better way of putting it than I had. In my opinion, that has been done, and more than once. Here's how I was looking at it:
Before the fortune-teller came along the 7 wives being cheated on were all thinking something like this: 'those poor 6 women who are being cheated on...how ironic that each of them is thinking "those poor 5 women who are being cheated on...how ironic that each of them is thinking '" those poor 4 women who are being cheated on...how ironic that each of them is thinking ""those poor 3 women who are being cheated on...how ironic that each of them is thinking '""those poor 2 women who are being cheated on...how ironic that each of them is thinking """that poor woman who is being cheated on...she doesn't have a clue!""" '"" "" '" " '
After the fortune-teller's remark, that last quote would suddenly become """that poor woman who is being cheated on...boy, I'll bet she's pissed now!"""
IOW, the regressing chain of "she doesn't know" is suddenly clipped off at the base, starting the domino chain.

I guess you can see now why I wanted a better way to state this.

[Schwartz]

this reminds me of the pumpkin farmer that kept losing pumpkins to thieves. To prevent further theft of his pumpkins, he placed a sign in the pumpkin patch that said, "One of these pumpkins has been poisoned." The next morning he went to his pumpkin patch. The sign had been changed. It now read, "Two of these pumpkins have been poisoned." hehe

[Ghost Post]

I believe the answer to this puzzle is 8, not 7... even if we assume that the coffin-maker does not get his orders until the men are actually dead.

The reason is that 8 full nights have passed in between the time the fortune teller came to town (during the day), and the time the coffin-maker got his orders (on the eighth morning after). As has already been explained, if there had been only one cheating husband, he would have been killed during that very first night after the fortune teller came. If there were two cheaters, they both would have been killed during the second night. Since there was an eighth night, that means there were eight cheating husbands, and therefore eight dead men, not seven.