This is one of the most amusing and elegant logic puzzles I've ever come across. Now, that's not saying much, because I don't go out looking for logic puzzles, but anyway... enjoy.

the well-hung natives puzzle:



My pleasure boat once ran aground on the Island of Noose, which is inhabited by primitive people who follow two strange customs. First, if a wife cheats on her husband, she tells everyone but him. And second, if the husband finds out that his wife has cheated, he hangs her at midnight in the public square, leaving her body dangling.

A friendly missionary, who had been teaching these primitives Western ways, was called back to the mainland. Before he departed, he summoned the natives together and told them: "Try to remember everything I've taught you. Go easy on the firewater, genuflect often, and remember the preferred position. And I must tell you, there's been cheating on this island." The missionary set sail before the heathens had a chance to question him.

Now I want you to tell me what is going to happen on the island. This is a tough puzzle. Although the solution covers every possibility, it is quite elegant. The solution should indicate how many natives will be hanged and when they will be hanged. Good luck.

some things to note: these natives are the masters of logic. that is, their logic is perfectly sound. also, solve the puzzle for if the missionary lied as well (as they have been known to do to God-forsaken island-bound native peoples).

so, you should know how many women were hung if 1 cheated, 2 cheated, etc... and if none cheated.

 

Although you didn't state it explicitly, I'll assume that after an unfaithful wife has told everyone else of her dalliance, none of them tells the cuckold. (It wouldn't be much of a problem otherwise.) Further, I'll assume that the natives will believe the missionary even when he lies.

Case one: the missionary told the truth

If only one wife has cheated there will be one husband who hasn't had another wife tell him that she's been frisky, so he'll know that it's his wife and hang her; this should happen immediately--that night.

If there were two cheaters, two men would each have heard on only one, and the rest would have heard of two. Those who have heard of two will do nothing. The two men who heard of only one will each watch the other to see if he immediately hangs his wife. When each sees that the other doesn't hang his wife, he will reason that the other had heard of exactly one cheating wife, and will then reason that the one report must have been about his own wife cheating. They'll both hang their wives the second night.

If there are more than two cheaters each man will have heard more than one report and have no reason to suspect his own wife: no hangings.

Case two: the missionary lied--nobody cheated

Each man, believing the missionary, will reason that he has not been told by another man's wife that she cheated, so it must be his own wife who did so. All of the men will hang their wives that night.

 

close! you were on the right track. here's the answer


personally, I've never been 100% happy with the answer because I think the original puzzle leaves out a few crucial bits (regarding the behavior of the natives in particular circumstances).

 

Pretty cool.

 

I see. If a husband heard from two cheaters, he would assume that the cheters would be hung on the second night. When that didn't happen, he would know that every husband had heard from two cheaters, and that meant there were three cheaters total, and his wife must be the third. Hence, three hangings the third night.

If a husband heard from three cheaters, he would expect all cheaters to be hung on the third night. When this didn't happen, he would know that all husbands knew of at least three cheaters, since they would have hung their wives if they had only heard of two. Therefore, each husband who hears from only three cheaters hangs their wife on the fourth night.

And so on. It isn't obvious from only n=1 and n=2.

 

if the missionary was lying, all the husbands believe it is their wife, they all show up at midnight, look around, realize they didn't hear about these other cheaters, and that they all must've thought the same thing-- that their wives cheated because they didn't hear of any cheaters. then they all go home, comforted by the fact that nobodys' wives cheated.

and remember, the missionary might not have been lying because it was with him that the wives did all the cheating!

 

[QUOTE]Originally posted by tritium_pie
and remember, the missionary might not have been lying because it was with him that the wives did all the cheating!

 

yes I am a weenie... people are hanged not hung

 

[QUOTE]Originally posted by PeaceLove&S2K

 

I know that, you know that, but I don't really care if I refer to capital punishment in the proper manner.