An isolated village had a thriving community who believed in the monogamous marriage of men and women. Like all good, isolated villages, it had a chief and believed in capital punishment. One aspect of the capital punishment was that any woman who discovered that her husband had committed adultery must kill their husband at dawn on the following day. And this particular village had another interesting facet: the women were obliged to share with all the other women in the village details of any crime they were aware of, except that they must not share their knowledge with the perpetrator or victim of the crime.
The chief became aware of a problem in his otherwise harmonious village: some of the men were having extra-marital affairs. He called a meeting of the whole village and announced that he knew of at least one man in the village who was committing adultery. He said no more.
What happened next?
Well, the first part of this problem is a “simple logical deduction”. We know there is at least one adulterous husband. Given that he is adulterous with a woman, that woman is obliged to share her knowledge of her own crime with all the other women apart from his wife. In this situation, the chief’s statement is a surprise only to the wife of the (only) adulterous husband, so she knows immediately it must be her husband, and dispatched him the next morning.
But what if there were two adulterous husbands? Well, in this case all the women in the village apart from the two wives would know of two adulterous men. The two wives would each know of only one – the other wife’s husband. They would therefore expect the other wife to kill her husband at dawn the next day. When neither does, they can logically deduce that the only alternative is that *both* their husbands are adulterous, and so, having missed dawn of the second day, would both kill their husbands at dawn on day 3.
You can see how this logic can be extended such that if there were 3 adulterous husband they would all be slain on the dawn of day 4, etc. etc.
But here is the logical twist. In all cases apart from the single adulterous husband, the chief’s statement doesn’t add any additional information into the system: every woman already knows that there is at least one adulterous husband. So, logically, how can his statement cause the results described above?