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 [quote="Kyp"]I understand the reasoning behind the progression of suspicious wives increasing one per night, but I see some unresolved issues: The proposition that the husband wasn't killed the first night has no justification .......suppose there was only 1 cheater? surely the progression would cease there. One suspicious wife, one dead husband...the progression hinges on there actually being more than 1 to prove there are 8 which is circular..what compells the wife to not kill her husband that same evenight ? Suppose all the wives get paranoid at once and kill their husbands after no result after 1 night, thinking they are the one being hoodwinked. Who says that for anyone to be killed, there has to be a cheater...isn't the paranioa enough? What if on the 3rd day, all these bodies turn up at once? Who says they cheated? So 1 person may die, they all may die, or any integer in between may die. The question is too ambiguous.[/quote]
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principessa
Posted: Sat Nov 18, 2000 12:25 am    Post subject: 1

you have to assume that no one dies the first six nights -- the riddle does not state this. this is the only way that all seven men will die on the seventh night.
the fortune teller stated that there was "at least one" man that was cheating. let's assume there WAS ONLY ONE man cheating. he would obviously die the first night b/c his wife would realize he was cheating -- subsequently, no one else would die the rest of the week...and so on for two cheating men, three cheating men, etc.

the only way one can arrive at the conclusion that seven men were cheating, and therefore seven men died, is to assume that no one died the first six nights. what if the fortune teller arrived on day eleven or day twenty? does the answer stay at seven men?
principessa
Posted: Sat Nov 18, 2000 12:18 am    Post subject: 0

you have to assume that no one dies the first six nights -- the riddle does not state this. this is the only way that all seven men will die on the seventh night.
the fortune teller stated that there was "at least one" man that was cheating. let's assume there WAS ONLY ONE man cheating. he would obviously die the first night b/c his wife would realize he was cheating -- subsequently, no one else would die the rest of the week...and so on for two cheating men, three cheating men, etc.

the only way one can arrive at the conclusion that seven men were cheating, and therefore seven men died, is to assume that no one died the first six nights. what if the fortune teller arrived on day eleven or day twenty? does the answer stay at seven men?
operageek
Posted: Sat Nov 18, 2000 12:17 am    Post subject: -1

you have to assume that no one dies the first six nights -- the riddle does not state this. this is the only way that all seven men will die on the seventh night.
the fortune teller stated that there was "at least one" man that was cheating. let's assume there WAS ONLY ONE man cheating. he would obviously die the first night b/c his wife would realize he was cheating -- subsequently, no one else would die the rest of the week...and so on for two cheating men, three cheating men, etc.

the only way one can arrive at the conclusion that seven men were cheating, and therefore seven men died, is to assume that no one died the first six nights. what if the fortune teller arrived on day eleven or day twenty? does the answer stay at seven men?
cha
Posted: Tue Aug 29, 2000 4:23 am    Post subject: -2

Kyp states "The proposition that the husband wasn't killed the first night has no justification .......suppose there was only 1 cheater? surely the progression would cease there."
The puzzle states that for a week every woman wondered if her man was faithful. If there were only one cheater, it would have ended after the first night and no one would have wondered after that. No ambiguity.
Kyp
Posted: Thu Aug 24, 2000 3:24 pm    Post subject: -3

I understand the reasoning behind the progression of suspicious wives increasing one per night, but I see some unresolved issues:

The proposition that the husband wasn't killed the first night has no justification
.......suppose there was only 1 cheater? surely the progression would cease there. One suspicious wife, one dead husband...the progression hinges on there actually being more than 1 to prove there are 8 which is circular..what compells the wife to not kill her husband that same evenight ? Suppose all the wives get paranoid at once and kill their husbands after no result after 1 night, thinking they are the one being hoodwinked.

Who says that for anyone to be killed, there has to be a cheater...isn't the paranioa enough?

What if on the 3rd day, all these bodies turn up at once? Who says they cheated?

So 1 person may die, they all may die, or any integer in between may die.
The question is too ambiguous.
RAH
Posted: Thu Aug 10, 2000 10:07 am    Post subject: -4

I'm new to all this and have a brief query. It doesn't actually say if men died any night in particular so what if there were only say 5 cheating husbands. After the 5th? night would it not stop. Therefore the coffin-maker would only have to make 5 coffins for 5 decyaing bodies.
Andy
Posted: Wed Aug 09, 2000 6:34 pm    Post subject: -5

I find it easier to illustrate with specifics - and from the coments here, I suspect some others would find it helpful also.

Case 1: 1 cheating husband
Suppose Arnold is the only cheating husband. Then Annie (his wife) doesn't know of any cheating husbands until she hears the fortune teller. She is then able to conclude that her husband must be cheating, so she kills him that night.

Case 2: 2 cheating husbands
Annie knows that Beth's husband Bob is cheating, but doesn't know of any others. She therefore expects that Beth is the only wife who didn't previously know about a cheater, so she expects Beth to reach the obvious conclusion and kill Bob that night. When Bob is still alive the next morning, Annie realises that Beth must know about another cheater - who can only be Arnold (annie would have known about any other one), so Arnold is a goner the second night. Beth, who already knew about Arnold, realizes the truth about Bob when Arnold survives the first night, so Bob also fails to wake up the second morning.

Case 3: 3 cheaters
Annie says to herself, "Beth's Bob and Connie's Carl will survive the first night, but not the second." (See case 2 for the reasoning that Annie imputes to Beth and Connie.) When Bob and Carl both survive the second night, Annie realizes that Case 2 doesn't apply; there must be a third cheater, who must be Arnold - so Arnold, Bob, and Carl die the third night.

Case 4: 4 cheaters
Annie expects Beth, Connie, and Darlene to kill Bob, Carl, and Doug the third night. When they don't, Annie realizes that there must be a fourth cheater - Arnold, of course. Beth, who knows about Arnold but not about Bob, expected Arnold, Carl, and Doug to die the third night - so all four men will die the fourth night.

Etc. On the sixth morning, all the women in the village know that there are at least 7 cheaters - and all but 8 know that there are at least 8. Annie, in particular, knows about 7 cheaters. She thinks that Beth knows about only 6, so she thinks about beth, "She knew about only 6 cheaters, but not about Bob. Now she must realize the truth about Bob, so he's living his last day." When Bob is still alive the next (seventh) morning, Annie realizes that Beth must have known about a seventh cheater. Since it couldn't have been Bob, and Annie knows about only 6 cheaters other than Bob, Annie realizes that the seventh cheater known to Beth must be Arnold. And so it goes.

Case 0 - the fortune teller was lying (or mistaken), and there aren't currently any cheating husbands in the village. All the husbands will go to bed confident of waking up the next morning - but they won't!
Ghost Post
Posted: Sat Aug 05, 2000 6:35 am    Post subject: -6

Limey wrote:
Quote:
I keep thinking that first and only conclusion you can draw is that there is one unfaithful husband, since every woman, with the exception of the one who is being cheated on, would know of him. The woman who was unaware of who the culprit is would have to come to the conclusion that it is her husband.

OK, so that woman (the wife of the single cheating husband) would kill her husband on the first night.

Now, imagine you are one of the wives. You know of that one cheating husband, and you've reasoned as you have above. You know that that man's wife will realize that, since she knows of no cheaters, the cheater must be her husband, and she will kill him the first night.

Now, after the first night, you see that he was not killed. The only way she could have failed to realize that her husband was cheating was if she knew of some other husband cheating. The only possibility, then, would be that your husband was cheating also.

So, after the first night, you know your husband is cheating. And likewise, she now knows her husband was cheating (by the same reasoning).

------------------------------------------------------------------------------------

Now, from the above, you can see that if there are two men cheating, their wives will realize it after the first night, and kill their husbands on the second night.

Now, suppose you (a wife) know of two cheating husbands. And suppose that after the second night, they have not been killed by their wives. We've already established that if there were only two cheaters, they would be dead after the second night. You know of two. There must be a third that you don't know of - your husband. So on the third night, you kill him. Likewise, they kill their husbands on the third night (because they, like you, knew of two cheating husbands, who they expected to be killed on the second night, unless there was a third cheater - their own husband).

Etcetera...

[This message has been edited by extro... (edited 08-05-2000).]
Ghost Post
Posted: Fri Aug 04, 2000 8:37 pm    Post subject: -7

also new here but i think no husbands were killed. The fortune teller is a fortune teller and therefore tells the future of peoples lives not the present (that would be a psychic or something, right?). He or she divulges information about husbands who will cheat in the distant future but not now, so although the wives know their husbands will cheat they cant kill them because they haven't cheated yet. New angle maybe but hopelessly wrong?
limey
Posted: Fri Aug 04, 2000 4:57 pm    Post subject: -8

I'm confused with those who come to the conclusion that there were zero husbands cheating or killed, and also by the deductive reasoning used by those arguing that seven were killed (one for each night).

First, believing that the number of men cheating is zero isn't consistent with the information provied in the riddle, since it clearly states in two places that there are. Early on it says "almost all" of the men are faithful. And it refers to the fortune teller's claim that there are unfaithful men as a "truth." So unless we're going to assume that the riddle contains false information, which would render every explination no more valid than any other, we can conclude that there is a least one unfaithful husband.

As for the logic that there is one husband killed for each day, I feel like I'm either simply not getting it or that the reasoning is flawed. I keep thinking that first and only conclusion you can draw is that there is one unfaithful husband, since every woman, with the exception of the one who is being cheated on, would know of him. The woman who was unaware of who the culprit is would have to come to the conclusion that it is her husband. But beyond that I'm not sure how it follows that there must have been a second man, then a third, a forth, etc.

Could someone please explain this to me?
some guy
Posted: Wed Aug 02, 2000 9:35 pm    Post subject: -9

DyfedG wrote:
[...]
For the men however, they were worried that the fortune teller may reveal names, so one of the philanderers (after a week of building up the courage) killed the fortune teller. Hence one man dead.
[...]
Why do you (and many others) assume that the fortune teller is a MAN? I suppose there is no law agains male fortune tellers, but whenever I picture a fortune teller I picture a woman!

The biggest mistake when dealing with any of these puzzles is to assume that the puzzle has any bearing on reality whatsoever. To find the solutions it is very important to remove as much friviolous detail as possible and not think in real-world terms, but instead in the pure abstration of logic and math. To try to see the real world in a puzzle will lead only to the folly.
Ghost Post
Posted: Tue Aug 01, 2000 10:12 pm    Post subject: -10

hmm..new here. well here's what i think: think that everyone in the town cheated since all of the men were afraid they were going to die. that makes all the men guilty.
Mercuria
Posted: Mon Jul 31, 2000 4:49 pm    Post subject: -11

Teddy
Posted: Sun Jul 30, 2000 11:46 pm    Post subject: -12

Well I belive that the answer to the puzzle infidelity is 0.I have some educated guesses behind this theory.Because if all women except the woman who's man is cheating on them is not aware because she is not told.So there fore if there was a cheating man the wife would not know about.The only people aware of it would be the other women in the village and the cheating man.Therefore as explained I belive the answer is 0 men are dead
DyfedG
Posted: Fri Jul 28, 2000 1:58 pm    Post subject: -13

The answer is one. As previously pointed out, the women knew before the arrival of the fortune teller of some cheating. The arrival of the fortune teller made no ral difference to them.
For the men however, they were worried that the fortune teller may reveal names, so one of the philanderers (after a week of building up the courage) killed the fortune teller. Hence one man dead.

Nice page, came across it by accident, unfortunately don't really have much time for this.
Mercuria
Posted: Fri Jul 28, 2000 4:56 am    Post subject: -14

page 3 =]
Ghost Post
Posted: Thu Jul 27, 2000 6:12 pm    Post subject: -15

Imagine two cheaters, and their wives, wife A and wife B.

Fact 1: Wife A knows there is at least one cheater.

But, the truth of "Fact 1" is not known to wife B. That is, Wife B does not know that Wife A knows there is at least one cheater.

When the fortune teller makes the announcement, in everyones presence, Wife B becomes aware of "Fact 1". That is, Wife B will then know that Wife A knows there is at least one cheater.

The announcement makes it "common knowledge" -
1) everyone knows it,
2) everyone knows everyone knows it,
3) everyone knows everyone knows everyone knows it,
4) ...

If there were two cheaters, everyone would know there is at least one, but not everyone would know that everyone knows that.

If there were three cheaters, everyone would know there is at least one, and everyone would know everyone knows it, but not everyone would know that everyone knows that everyone knows it.
Quailman
Posted: Thu Jul 27, 2000 12:46 pm    Post subject: -16

I'm starting to believe zero, because all the women already knew there were some number of cheaters. Either they knew the exact number (which didn't include their husbands), or they knew one less than the total (which did include their husbands). What new information did the fortune-teller really provide?
boris
Posted: Thu Jul 27, 2000 12:31 pm    Post subject: -17

the answer is 0 because the riddle already like says it and u just have to use common maths to work it out
carebear
Posted: Wed Jul 26, 2000 10:54 pm    Post subject: -18

I'm not sure if this makes a difference, but the original puzzle states that the CW MIGHT find out that her husband is cheating on her through observation or whatever. If this happens, wouldn't that throw off something in the solution? I wasn't sure if anyone touched on this already, but it didn't make sense to me.
da_warped_1
Posted: Wed Jul 26, 2000 7:14 am    Post subject: -19

i still think its 0 or zero

One fateful day a fortune teller came to town and revealed the terrible truth: some man or men had been unfaithful.

well it also says that some man or men had been unfaithful.. had !!
so this means that it could of happened ages ago and maybe even the wife killed the man already

l8terz: jezz

cha
Posted: Wed Jul 26, 2000 5:25 am    Post subject: -20

Oops - I forgot the wording of the original question - If the coffin maker was a cheater, there would be nine coffins ordered, but no dead men on the eighth day. OK, I think I'm done.
cha
Posted: Wed Jul 26, 2000 5:18 am    Post subject: -21

So... have we figured this one out yet? The answer is eight if there are eight dead bodies on the eighth morning, and nine if the coffin maker is a cheater and one of the wives places the order for coffins in preparation for nine bodies on the ninth morning. The only other tidbit I can speculate on is that if the men don't communicate as well as the wives, then none of the men know how many cheaters there are. This means that if a man places the coffin order, there will be eight (one for each dead body on the eighth morning). If a woman places the order, there could be nine, if the coffin maker is unfaithful. If this is the case, then each cheating husband will know he has been discovered and would be well advised to get the H*** out of Dodge before nightfall.
Ghost Post
Posted: Tue Jul 25, 2000 2:38 pm    Post subject: -22

Yeah, just consider the case of one cheater. Once the announcement is made, his wife will immediately know.

Then consider two cheaters. Each of their wive's knows there is at least one cheater, and they know that if there is only one, his wife will immediately realize. If his wife does not realize, on the next morning, each one will realize there must have been more than one cheater, and realize her own husband is cheating.

Similarly for three. Each cheaters wife knows of two cheaters, and knows, by the previous line of reasoning, that if there are only two cheaters, their wives will have killed their husbands on the second night. If the following morning comes and nobody was killed, then each knows their are more than two.

Etc...
Coyote
Posted: Tue Jul 25, 2000 3:22 am    Post subject: -23

dpgendron, are you the Icarian version of da_warped_1 ?
The proof you gave left out one critical fact...the fortuneteller's remark insured that every woman in the village knew for a fact that every other woman knew someone was being cheated on.
Ghost Post
Posted: Tue Jul 25, 2000 2:56 am    Post subject: -24

restated - the answer is zero. I concur.
cha
Posted: Sun Jul 23, 2000 4:11 am    Post subject: -25

A woman can "learn" her husband is cheating through gossip, by witnessing, by being a participant in the act, or by using the logic that has been described many times above.
da_warped_1
Posted: Sat Jul 22, 2000 11:38 pm    Post subject: -26

the answer is 0 or zero
ill prove it too you now!!!
this is what th riddle says
"Slightly germane as well is the long standing tradtion that if a woman ever learns her husband is unfaithful, she will kill him that night while he sleeps".
the key word here is "learn"
it also says
"It also may be relevant that the women are notorious gossips. If a woman discovers a man to be untrue, either on her own or through heresay, this fact will quickly be known throughout the village within a matter of hours to all the married women except the wife of the unfaithful man".
the key words here are.... either on her own or through heresay, this fact will quickly be known throughout the village within a matter of hours to all the married women except the wife of the unfaithful man

So now the anwser will be zero because the women of the unfaithful men never finds out
everyone else will know but not her.. she can only kill him if she finds out herself..

so thats my answer = 0

lat3rz: jezz
Jess Terr
Posted: Fri Jul 21, 2000 3:10 pm    Post subject: -27

Rune:

The sequence here doesn't go: 1 man the first night + 2 men the second night, etc.
The sequence is: 1 man the 1st night OR 2 men the 2nd night OR 3 men the 3rd night, etc.
Ghost Post
Posted: Thu Jul 20, 2000 5:51 am    Post subject: -28

hehey all
I just dropped by, and well i must say that i like puzzles. i may not be the greatest mind, nor even close to it. but it seems that everyone makes assumptions within their answers. it is a very difficult question indeed. and i myself have an answer or 2 of which i am curious of. tell me what u think of it.
1. some of u said earlier that night 1, 1 man dies, night 2, 2 men die and etc until the day where the grave guy is told to build the caskets right. if that the case then what about this....1+2+3+4+5+6+7 and another +8 for those who believe the eighth night thing. so that would make either 28 or 36.

2. this one however may seem quite odd. it is that all the husbands die. odd indeed eh?
well, it is known that any wife who knows her hubbs be cheatin will be killed. however she will never hear it from the other wives that he was cheating. with that being the case, even if she hears of 6 others cheating, she will still know that no other wife would tell her if she is the 7TH wife who has a hubby cheatin on her or not. and if they kill based upon gossip then all wives would fear their men of cheating and kill them the first night. (abstract) i kno,
but it is food for thought.
: )

and another thought. i kno i said 2 but this is the last one.
another solution could be none.
based upon assumption of course. b/c all the wives except for the one being cheated on would know of the husbands deed. this would be the case before the fortune teller interferes. even after the interference of the teller, they would still all kno the same and would not expect it to be their hubby's due to the fact that they know of the others who are cheating and would therefore go on with their merry lives.
lates
cha
Posted: Thu Jul 20, 2000 4:12 am    Post subject: -29

First, no wife assumes her husband is faithful. Each wife knows to keep a man's cheating a secret from his wife. She would therefore assume all others would do the same with her. If she knew of one cheater, she would not assume her mate is faithful, but would recognize that no one would tell her if he wasn't. Second, apparently, the fidilety of the husbands is important tothe wives, as each wife is willing to kill her husband based on gossip. So - the wives could create their own common knowledge situation if they so chose. As soon as any one woman learned of two cheating men, she could publicly announce that there was at least one cheating male. This would not be giving anyone any extra information, as all the wives would already know this. At this point the countdown would begin and on the second morning after the announcement there would be two dead husbands. This would serve as much more of a deterrent, as only one husband at a time would ever be able to cheat and live. As soon as the second husband was caught, both would die.
dpgendron
Posted: Thu Jul 20, 2000 3:21 am    Post subject: -30

The answer is Zero. Let me explain.
For a whole week every philandering man worried. In a world where the gossip spreads in hours AND a woman spouse kills that night, if EVERY philandering male was worried all week even if every means one, the puzzle solves itself. The cheater was never exposed.
Ghost Post
Posted: Wed Jul 19, 2000 2:26 pm    Post subject: -31

For Ewan and Burning, regarding the definition of common knowledge:

If X is common knowledge,
then not only does everyone know X and everyone know that everyone knows X,
but, everyone knows that everyone knows that everyone knows X, etc...

Without using "etc...", X is common knowledge if everyone knows X and everyone knows that X is common knowledge.

There is an important logical distinction, though it seems somewhat blurry.

If there were one cheater, not everyone would know there is at least one cheater.

If there were two cheaters, everyone would know there is at least one, but the wives of the cheaters would not know if there were one or two, and hence would not know that everyone knows there is at least one cheater. So with Ewans definition of common knowledge (everone knows, and everyone knows that everyone knows), with two cheaters there is not common knowledge that there is at least one cheater.

If there were three cheaters, everyone would know there is at least two. And since with two cheaters, everyone knows there is at least one, then if everyone knows there are at least two, everyone knows that everyone knows there is at least one. So with three cheaters, by Ewans definition of common knowledge, with three cheaters there will be common knowledge that there is at least one cheater.

But, with three cheaters, not everyone would know that everyone knows there are at least two, and so not everyone would no that everyone knows that everyone knows that there is at least one.

And no matter how many cheaters, it never becomes common knowledge in the general sense. But when the fortune teller arrives and announces, in front of everyone, that there is at least one cheater, everyone hears the announcement, everyone knows that everyone else heard it, and knows that everyone else knows that everyone else heard it, etc...

Ghost Post
Posted: Tue Jul 18, 2000 10:07 pm    Post subject: -32

I believe that NONE were killed. Observe:
"a woman ever learns her husband is unfaithful, she will kill him that night while he sleeps." and gossip goes "to all the married women except the wife of the unfaithful man."
The woman who's man was unfaithful would not know if he was unfaithful and to kill him in the middle of the night.
Coyote
Posted: Tue Jul 18, 2000 9:07 pm    Post subject: -33

Thanks, NaughtyJ! I guess I should have taken the time to read all the posts in this thread, then I would have seen that!
Naughty J
Posted: Tue Jul 18, 2000 3:26 pm    Post subject: -34

To Coyote! The answer to your question about the fortune teller is that for the counting of days to occur, a starting point is needed, and the fortune teller's remarks re-set the clock to zero, so to speak. If there is one cheating husband, the remarks give new information to the one wife who's never heard about anyone cheating. If there are two cheating husbands, it gives each of their wives a starting point from which to wait a night to see if anyone kills their husband. When nobody does, they realize their husband cheats. The same happens for all larger integers. Prior to this information from the fortune teller, there was no one, apparently, who said "we all know." Thus there existed no way for the collective to be sure the collective was counting starting on the same day, and so no way to solve the riddle.
Dragon Phoenix
Posted: Tue Jul 18, 2000 4:32 am    Post subject: -35

on drugs again, Extro?

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XXXXXX rude sig censored by forum monitor
Ghost Post
Posted: Tue Jul 18, 2000 3:07 am    Post subject: -36

3.141592654777777777777777777777777777........

cauliflower
HyToFry
Posted: Mon Jul 17, 2000 10:38 pm    Post subject: -37

Oh woops, sorry I didn't mean for that to be rude, if anyone (especially Arkive) took it that way i'm soowrry.

Read it again and imagine me in a light hearted mood. I'm always like that, so if i seam snippy or rude, its just the damn internet not letting my express my TRUE feelings again.
Borodog
Posted: Mon Jul 17, 2000 10:23 pm    Post subject: -38

Hmm . . . somebody piddle on your corn flakes, Hy?

AKA (All kidding aside), I think all the women certainly do know. By the problem statement, we can interpret that when a woman cheats with a man, she immediately tells all of the other women about it (braggart), with the exception of the wife of that man.

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Insert humorous sig here.