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Logic riddles


November 4 2011

There is a classic logic puzzle out there which is often not worded correctly. The puzzle is often worded like this:
There is a small village with 1 priest and 7 heterosexual couples. In this village, all 7 men have committed adultery, and all women know it when anyone besides their husband has committed adultery. The law of this village is that the penalty for adultery is immediate divorce.

The priest knows about all the adultery that has happened because he has heard all confessions. One Sunday morning, during his homily, he tells the entire village that there is at least one adulterer in the town.

What happens?

The correct answer (for this wording) is that nothing happens.

In more detail, here are the seven wives and how many adulteries they know about:

NameKnows about # adulteries
Now, when the priest says: "There is at least one adulterer in the town", the women look at each other, giggle, and think to themselves "Of course. Indeed, there are six adulterers". The priest has merely shared information that everyone already knows.

If there was only one unfaithful man, the wife would immediately know they were unfaithful and the divorce lawyers would get a call. In the case of two or more unfaithful couples, nothing happens, except for a bad feeling about the moral decay of the village.

If the priest were to say "there are at least two unfaithful couples" in a town with two unfaithful couples, then there would be two divorces. If the priest were to say "there are two or more unfaithful couples" in a town with three or more unfaithful couples, there would be no divorces.

Yes, there are logic puzzles out there where the correct answer is not the intuitive answer (You're on a game show. There are three doors, only one of which hides a prize. You choose a door. The host opens a door without a prize, and tells you that you can change the door. You, unintuitively, should always change the door). This isn't one of them.

Update Looking more closely, it appears that the great Raymond Smullyan himself originally posed this puzzle. That in mind, yes, the women will figure out the adultery going around if:

  • All the women are righteous and honest, and therefore would immediately file for divorce if they can show that their husband is unfaithful.
  • All the women know that every single other woman in the village is likewise righteous and honest.
Of course, if this were true, the village can never have more than one married adulterer, unless all of the adultery happens at once in a single drunken night. Or the puzzle can work if the women will only divorce their husbands for adultery when the priest calls upon his faithful to do so.

This is akin to the "-gry" problem, worded like this:

"Angry" and "hungry" are two words in the English language that end in "-gry". What is the third word. This is a puzzle which requires you to read carefully. So, what is the third word?
The answer is "what" -- the first "What is the third word" is a statement, not a question. Alas, people remember the question wrong and it becomes:
"Angry" and "hungry" are two words that end in "-gry". What is the third common English word that ends in "-gry"?
The answer being that "angry" and "hungry" are the only words in modern English with a "-gry" ending.

The point being: If a riddle like this is not correctly worded, the answer changes.

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