An interesting logic problem

A friend of mine sent this to me via e-mail:

It seems that this church missionary visited a small island in the South Pacific. The natives were exotic looking and all very atheletic. They did, though, have one strange custom that the missionary found baffling. If a woman cheated on her husband, she told everyone on the island except him. And if he found out about it, she'd be hanged in the village center at midnight.

The missionary did his work and when he was about to leave, he told the assembled villagers, "I have immensely enjoyed my time with you. Remember to read the Good Book and think of our Lord's sacrifice for you. Oh, and I should tell you, there's been some cheating happening on this island." Before he could be questioned further, he took off on his boat, leaving behind the baffled villagers.

So how many women were hanged in the village center?

Insufficient data.

According to him (my friend, that is), it would depend on how many cheated (if any).

If one woman cheated, then one man (her husband) on the island doesn't know about it. Since he knows of nobody, she gets hanged at midnight. If two women cheated, then two men (their husbands) know about the other woman cheating. So in the morning, they would expect to see that other woman hanging. Since nobody is, they must conclude that more than one woman is cheating. Since they only know about one, two women get hanged that night.

If the missionary was just lying for his own amusement (or for whatever reason) and nobody was cheating, then every married man in the village would show up that night to hang his wife. They would, of course, see everybody else there and everyone would reassure each other that no cheating was happening. And, very probably, the next missionary to visit would be hanged instead.

Like I said. Insufficient data.

Why would only the women get hanged, what happened to the man they cheated with? It seems likely this practice was set in place by the men of the Island as it would certainly discourage women from cheating but not discourage the men from trying to get them to cheat.

Likely any woman who did cheat told no one, why would she as it essentially meant the death sentence for her. The chances of the husband not finding out if everybody else knew is almost nil. The missionary was a man so by making that statement he inferred some wife slept with him, so they should have hung him as well.

My response would be none. There were no specifics given and no husband had definite proof that his wife had cheated. The minister merely followed the custom of the island by telling everyone, but left out the specifics.

None cos it was two men were cheating, with each other

Pink is right. The clue here is the "baffled villagers." You have to look at the underlying conditions. If all of the wives had cheated, then everybody would have already known that cheating was going on, but the missionary would have given no new info, and no one would have been hung, BUT they would not have been baffled. The same thing would have been true if there were more than one cheating wife. If there were only one cheating wife, then the new information (new only to the cheated-upon husband) would cause that one wife to be hung, but again, no one would be 'baffled' by this. If no wife had cheated, then initially every husband would assume he had been cheated upon, but it would quickly become apparent, when every husband planned to hang his wife, that the feared adultery had never taken place, or everyone else would have known. The would indeed be baffled. Only if there were male homosexual adultery would there be no way for everyone else to know, assuming they followed the customs. And this would be baffling to the islanders (the same as if there had been no cheating). Since there was no custom causing husbads to report their cheating, I would go Pink one better and say the reason the missionary knew about the cheating was that he was involved in it. Even if the villagers figured it out eventually, there would be noi cheating wife to hang.

Was the missionary male? From the use of "he" and "his work", I think I can assume this. It is possible the missionary came to the island with his wife (or married a local woman). If she was left behind and the missionary's comment was taken as personal, she might have got hanged. Before I checked back the language and found it did imply the missionary was male, I did consider that the missionary might be the cheating wife - in which case, the answer would be none because she'd got away in time.

If the missionary is not personally involved, then as he said "some cheating", which doesn't mean they were all cheating, the answer would be none, unless the husbands exchanged information.

All this, of course, depends on the unlikely premise that no-one would lie.

Since the cheating wife has to tell everyone on the Island, why would the villagers be "baffled"? In the normal course they would already know who it was ( the rule is the cheating wife must tell EVERYONE) and since they would all know and the missionary just told the husband---he was in the assembly, presumably---the conditions have been met to hang the wife or wives and everyone knows who they are. But we return to "baffled villagers". That means that they don't know because the cheating wife told only one person, the missionary; or nobody cheated because the missionary made it up. Either way the missionary did not name the cheater, the custom was not followed because the cheating wife did not tell everyone, hence no one knows who it is, if anybody. Nobody hangs.