Infedelity

[HyToFry]

You've misread, it says a week passes, then... blah blah....
it was on the 8'th morn that the coffin maker got his orders, I'm thinking that 8 men died that night, others are saying 7 the previous night (before the orders were given). oddly enough BOTH make sense, but I'm going with eight because I always take the "other" answer when there is more than one.

[Ghost Post]

I'm arguing that 8 men died just *before* the morning when the coffin-maker got his orders.

[HyToFry]

WOW!!! good point, eight it is, for those of you that subscribe to the orders being placed after the deaths, and nine for me and any of my followers that say the orders were placed before the men were killed, in either case seven is WRONG.

Its Eight, thats the answer, but I'm with nine cuz i'm different.

GOOD JOB Ghoul, We all thought this was solved, we were WRONG, DEAD WRONG

[HyToFry]

For those of you that still don't get it

[Tom]

If you are of the opinion that the orders were placed before the men were dead, the answer is zero.

[Ghost Post]

Thanks, Coyote. I get the idea now. I misunderstood the problem as being that there might be some women who did not know that everyone knew that infidelity is going on. That is not the case. The problem is that not everyone knows that everyone knows that everyone knows that infidelity is going on. Until the general announcement. Yoiks.

[Eamonn Magrath]

Ghoul ... surely there weren't 8 nights? The eight would perhaps be due on that night ... I know what you mean ... 'on the eight morning after' ... does it include, or not, the morning of visitation?

[HyToFry]

'AFTER' would be EXCludeing it, so there WERE eight nites. and eight dead. (or zero if you subscribe to my bull crap theory)

[Ghost Post]

Two things pop up that interest me:

1) It does not explicitly state that the women of the village know for *certain* of all of the unfaithful husbands. It merely states that if they find out (or commit the deed themselves) that word will spread quickly.

2) It also does not state that the husbands exclusively have affairs with women of the village, although it is assumed.

With this being the case, is it possible that the number of dead husbands can not be calcualted by us, since the actual number of dead husbands is equal to the *known* number of unfaithful husbands (unless someone on this board is married to a faithful husband in the village . Just wondering...

Jeff

[Ghost Post]

Two things pop up that interest me:

1) It does not explicitly state that the women of the village know for *certain* of all of the unfaithful husbands. It merely states that if they find out (or commit the deed themselves) that word will spread quickly.

2) It also does not state that the husbands exclusively have affairs with women of the village, although it is assumed.

With this being the case, is it possible that the number of dead husbands can not be calcualted by us, since the actual number of dead husbands is equal to the *known* number of unfaithful husbands (unless someone on this board is married to a faithful husband in the village . Just wondering...

Jeff

[HyToFry]

1) yes it does.

[daniel801]

if you're the 8th cheater and it's coming up on the eight day, then you had better start another affair with someone

[Quailman]

For any number of cheating men, N, there are a lot of women who know that there are N cheaters, and there are N women who know that there are (N-1) cheaters. They all know that there are two possibilities, and they all assume themselves to be among the many (rather than the N). When the (N-1) morning arrives and no husband is dead, then they now know that there are at least N cheaters, and that their husband is the one that they need to add to their own knowledge base to get to N. Thus, on the Nth morning, N husbands will be late.

On the eighth morning, there are eight coffins required.

[Ghost Post]

Thank you Hy for quoting a portion of the puzzle that clearly shows that point 1 of my previous post is true It explicitly states *IF* a woman of the village finds out of a cheating husband that it will quickly spread. It does *NOT* say that every infidelity in the village will be discovered. Also, the reason point 2 is valid is because if the cheating husbands all had affairs with women of the village, then point 1 would be irrelevant since the women of the village *would* know of all of the cheatings. Please reply if you need me to clarify further.

[Ghost Post]

In all fairness though, my points are fairly irrelevant anyway seeing as the puzzle asks for the number of dead men, not the number of cheating men.

[HyToFry]

Your points would be valid though... picky but valid. In fact VERY picky. I'll show you some more picky things you could say about the riddle, but the riddle is told and interperated, we really shouldn't do alot of picky things..

Lets say 50 men were cheating, on the eigth night 1 woman dies in her sleep (of old age, or whatever) on the eighth morning the coffin makers orders would be "Build one coffin for poor widow jenkins (she already killed her husband 32 years ago) so there would be zero men dead, or maybe noone died and the coffin makers orders were "build no coffins"

But these are picky points and we assume that the woman do in fact know of all of the cheating that goes on.

[Borodog]

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.

[HyToFry]

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.

[Ghost Post]

3.141592654777777777777777777777777777........


cauliflower

[Dragon Phoenix]

on drugs again, Extro?

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XXXXXX rude sig censored by forum monitor

[Naughty J]

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.

[Coyote]

Thanks, NaughtyJ! I guess I should have taken the time to read all the posts in this thread, then I would have seen that!

[Ghost Post]

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.

[Ghost Post]

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...

[dpgendron]

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.

[cha]

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.

[Ghost Post]

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

[Jess Terr]

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.

[da_warped_1]

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

[cha]

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.

[Ghost Post]

restated - the answer is zero. I concur.

[Coyote]

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.
Please read all the posts in this thread and re-examine your logic...I believe you've made an error.

[Ghost Post]

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...

[cha]

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.

[cha]

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.

[da_warped_1]

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

[carebear]

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.

[boris]

the answer is 0 because the riddle already like says it and u just have to use common maths to work it out

[Quailman]

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?

[Ghost Post]

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.