Re: Cryptic Puzzles and Riddles
Oops! Didn’t see this, I promise!
Re: Cryptic Puzzles and Riddles
Okay my turn!
This problem was given in a UMD class last year (by Professor Brin (Sergey Brin's (founder of Google) dad)), and we obsessed over it when we heard it. Good luck!
Imagine a very puritanical town where everyone is married.* There are only husbands and wives (zomg heteronormative). - If a husband finds out that his wife has been unfaithful, he cuts off her head that night, at midnight - If a wife cheats on her husband, the husband grows horns from his head (weird old European superstition)
The husband does not know if he has horns on his head.* In this town, touching your forehead is considered bad form.* No one gossips either.* No husband knows if he has horns on his own head, but he can see it on others.*
A traveller comes to town, spends a few days, and during this time, is so grievously insulted that he wants revenge.* He calls the whole town to a meeting and says to them, "Some of you have horns."* And promptly leaves.
At that time, there were 20 husbands in town with horns on their heads.* Twenty days after the traveller leaves, 20 wives are dead.*
The question is:* If everyone could see the horns on each others' heads, why did the traveller's comment touch off the murder spree?
Thinking....I think I can answer now but need to tie up a loose knot there or close other possibilities.
Let me answer you in PM. I think I have the answer and why. Let me know if my reasoning and assumption from the question is correct.
Re: Cryptic Puzzles and Riddles
Come on, folks! 
Re: Cryptic Puzzles and Riddles
nice one! i have worked that out...but I guess articulation would be the issue here.
While they could see everyones horns - no one was sure whether they had horns. So the visitor announcement came as a sort of trigger.
Now why did they commit murders at the end of 20th day -
Depending on whether he has horns or not - any person would see either 19 or 20 horns. If the person who sees 19 horns would surely come to know at the end of 19th day if he has horns or not by checking if there was a slaughter in the village. because if there were only 19 horns then all the 19 would have worked on 18th day whether they had horns or not
did i make sense!
Re: Cryptic Puzzles and Riddles
^you're on the right track, but like you said, not fully articulated.
Re: Cryptic Puzzles and Riddles
my head hurts 
I’ll give it a go in the morning, pwomise!
Re: Cryptic Puzzles and Riddles
*The official answer: *
If there was one husband with horns, he would look around, see no one else with horns, and know that his wife's a ho, and she would die that first night. He had no reason to suspect anything before the traveler said what he said, because he saw no one else with horns.
If there were two, both of them would only see each other, and would assume that the other guy must be the only guy with horns. They would therefore expect the other guy to kill his wife the first night. The next day, when neither wife is dead, each husband would realize that he has horns, because the other guy did not kill his wife the night before because he saw another man with horns. Both wives would die the second night.
If there were three, each would logically expect two wives to die the second night, as explained above. When they don't, then each of the three realizes what's up on Day 3, and kills their wives that third night.
And so it goes... the men of the town understand this logic. There are n husbands with horns, and each of them can see n-1 others. When the n-1th night passes with no murder, then every single husband with horns would realize on the nth day that there is in fact 1 more husband with horns than the number that they can see, and that means it must be himself. After coming to this epiphany, all n husbands kill their wives on the nth night.
Re: Cryptic Puzzles and Riddles
*The official answer: *
If there was one husband with horns, he would look around, see no one else with horns, and know that his wife's a ho, and she would die that first night. He had no reason to suspect anything before the traveler said what he said, because he saw no one else with horns.
If there were two, both of them would only see each other, and would assume that the other guy must be the only guy with horns. They would therefore expect the other guy to kill his wife the first night. The next day, when neither wife is dead, each husband would realize that he has horns, because the other guy did not kill his wife the night before because he saw another man with horns. Both wives would die the second night.
If there were three, each would logically expect two wives to die the second night, as explained above. When they don't, then each of the three realizes what's up on Day 3, and kills their wives that third night.
And so it goes... the men of the town understand this logic. There are n husbands with horns, and each of them can see n-1 others. When the n-1th night passes with no murder, then every single husband with horns would realize on the nth day that there is in fact 1 more husband with horns than the number that they can see, and that means it must be himself. After coming to this epiphany, all n husbands kill their wives on the nth night.
I do not think above answer and logic makes sense.
Here is why:
The question says when the guy said some of you have horns, there were 20 husbands with horns. He had called people to gather right? So why they all did not see each other horns then at the same night? Why one night by one night?
Anyhow, there is no reason why any husband with horn would definitely have his wife as a ho or cheater.
The horn simply means HE is the cheater.
There is no sure way to tell which woman is a cheater since women were not supposed to have ANY sign of being cheaters and ONE woman may cheat with ALL 20 men and still have 20 men develop horns.
Also the question did not say there were ONLY 20 couples. So these 20 men would have cheated with the men who did not cheat and would not have develop horns.
Lets assume there were 60 couples. And we can assume any number since it is not mentione in the question at all. So 20 men who cheated could have cheated with any of 60 wives and still these wives would not have been found by their respective non-cheating husbands.
Ther are other points which make this question and its answer invalid including why should there be one by one night husband would have found his wife was a ho. I read your uestion and then answer again and it did not make sense at all.
Essentially, the question should have been made by keeping some loop holes in mind. Sorry if you still feel the question was great. But it was not.
Am I missing something here? :)
Re: Cryptic Puzzles and Riddles
Diwana, it took me a while to understand it too. It's actually a math problem.
It's not 20 men who have cheated; it's 20 wives. The horns happen when the wife cheats.
Here's how mt friend explained it:
Suppose only one man has horns on his head. Then when he looks around the town and sees no one else with horns, and the traveler said that at least someone does have horns, then he can conclude that he has horns and kills his wife that night.
Now suppose there are two men with horns. Each knows that the other has horns, but is unsure between the cases (a) wife is not a cheater and only one man has horns and (b) wife is a cheater and he too has horns. So the first night, if it were the case that only one man has horns, then we go to case one, and there is one woman dead that night. However, if one day passes with no death, then on the second day the husbands know that it's not case 1, so there must be at least two. Since they saw only one man with horns in the village, that means the second must be him. So on the second night, two women are killed, because each husband realizes that he too must have horns (which is why the other guy didn't kill his wife the first night).
You can follow the same logic for N=20. The reason the traveler's comment touches off the murder spree is because there is no confirmation that anyone has horns (think of case 1). Once he confirms it, then the husbands begin to deduce whether they have horns or not.
Re: Cryptic Puzzles and Riddles
Diwana, it took me a while to understand it too. It's actually a math problem.
It's not 20 men who have cheated; it's 20 wives. The horns happen when the wife cheats.
Here's how mt friend explained it:
Suppose only one man has horns on his head. Then when he looks around the town and sees no one else with horns, and the traveler said that at least someone does have horns, then he can conclude that he has horns and kills his wife that night.
Now suppose there are two men with horns. Each knows that the other has horns, but is unsure between the cases (a) wife is not a cheater and only one man has horns and (b) wife is a cheater and he too has horns. So the first night, if it were the case that only one man has horns, then we go to case one, and there is one woman dead that night. However, if one day passes with no death, then on the second day the husbands know that it's not case 1, so there must be at least two. Since they saw only one man with horns in the village, that means the second must be him. So on the second night, two women are killed, because each husband realizes that he too must have horns (which is why the other guy didn't kill his wife the first night).
You can follow the same logic for N=20. The reason the traveler's comment touches off the murder spree is because there is no confirmation that anyone has horns (think of case 1). Once he confirms it, then the husbands begin to deduce whether they have horns or not.
I hate to spend a lot of time on this question and sound argumentary but with all due respect, I still do not agree with the background and logic of the question/answer. This post of yours has flaw and not what the question had.
Like I said before, the question was created by someone who did not think of ALL possibilities.
We do not have to continue this discussion since the spirit of the thread is fun and not to sound arguing.
Lets just say we agree to disagree. Thank you. :)
P.S. We can discuss this in PM if you wish.
Re: Cryptic Puzzles and Riddles
I'm not taking it personally, as I didn't create the question (if I had, the riddle would involve word play, not math :p) . I don't understand the point of confusion, tho.
Re: Cryptic Puzzles and Riddles
I do not think above answer and logic makes sense.
Here is why:
The question says when the guy said some of you have horns, there were 20 husbands with horns. He had called people to gather right? So why they all did not see each other horns then at the same night?
yes they saw the other horns, but they did not see their own horns.
[quote]
Why one night by one night?
Anyhow, there is no reason why any husband with horn would definitely have his wife as a ho or cheater.
[/quote]
not initially, no.
[quote]
The horn simply means HE is the cheater.
[/quote]
No. It means the wife cheated. I think you've misread the riddle.
[quote]
There is no sure way to tell which woman is a cheater since women were not supposed to have ANY sign of being cheaters and ONE woman may cheat with ALL 20 men and still have 20 men develop horns.
[/quote]
the cheaters don't get horns; the husbands get horns. this us a basic misreading. It doesn't matter who she slept with; only her husband gets horns.
Re: Cryptic Puzzles and Riddles
yes they saw the other horns, but they did not see their own horns. not initially, no. No. It means the wife cheated. I think you've misread the riddle. the cheaters don't get horns; the husbands get horns. this us a basic misreading. It doesn't matter who she slept with; only her husband gets horns.
Sighs.
The answer is still wrong because there is not reason whatsoever for any husband to think his wife is a cheater if others did not kill their respective wives.
There is no limit to how many couples are there. And there is no way ANY husband has to suspect HIMSELF as having horn. He just cannot know as the question says. Between two men with horn, one memeber will never be able to suspect he is the one with horn so there will be no reason for him to wait let alone kill his wife.
How can one be so sure he is the one with horn and he is the one who's wife is a cheater when no one can tell him and he cannot find out by touching it or women do not have any physical change if they cheat.
Let us not make others bored of our discussion from now on. Please talk to me via PM.
I am so ready for another question. :)
Re: Cryptic Puzzles and Riddles
Above question and answer reminded me this old question. :D
Here is for you to get entertained and make a comment.
Three friends have a nice meal together, and the bill is $25.
The three friends pay $10 each, which the waiter gives to the Cashier.
The Cashier hands back $5 to the Waiter.
But the Waiter can't split $5 three ways, so he gives the friends one dollar each and keeps 2 dollars as a tip.
They all paid $10 and got $1 back. $10-$1 = $9
There were three of them 3 X $9 = $27
If they paid $27 and the waiter kept $2: $27+$2=$29
*Where did the other dollar go? *
Re: Cryptic Puzzles and Riddles
They paid $27, two dollars above the bill total, which means the waiter has a $2 tip. So there isn't an extra dollar.
Re: Cryptic Puzzles and Riddles
*If they paid $27 and the waiter kept $2: $27+$2=$29 *
See if you want the question to be logical than the above statement is incorrect because they paid $27 which includes the $2 tip its not on top of the $27. Sahar's answer is right though because the bill was $25+$2(tip)+$3 (each got a dollar back) = $30!
Re: Cryptic Puzzles and Riddles
They paid $27, two dollars above the bill total, which means the waiter has a $2 tip. So there isn't an extra dollar.
Exactly.
See if you want the question to be logical than the above statement is incorrect because they paid $27 which includes the $2 tip its not on top of the $27. Sahar's answer is right though because the bill was $25+$2(tip)+$3 (each got a dollar back) = $30!
Yes.
The way the question was asked was to make some people confused. :)