# Every man in a village has cheated on his wife

Every wife in the village instantly knows when a man other than her husband has cheated, but does not know when her own husband has.

The village has a law that does not allow for adultery.

Any wife who can prove that her husband is unfaithful must kill him that very day.

The women of the village would never disobey this law.

One day, the queen of the village visits and announces that at least one husband has been unfaithful.

What happens?

Once all the wives know there are at least 1 cheating husband, we can understand the process recursively.

Let's assume that there is only 1 cheating husband. Then his wife doesn't see anybody cheating, so she knows he cheats, and she will kill him that very day.

If there are 2 cheating husband, their wives know of one cheating husband, and must wait one day before concluding that their own husbands cheat (since no husband got killed the day of the announcement).

So with 100 cheating husbands, all life is good until 99 days later, when the 100 wives wives kill their unfaithful husband all on the same day.

 DifficultyHard TypeLogic

Agreed, that one was hard.
- Glaive Lord (8 Aug 2013)

IMO, all men will be killed at the very day the queen unveiled about cheating.

Since every woman knows about other woman's husband and, as stated, all men of that village have cheated their wife, that means every woman is aware of 99 extra-marital affairs. Since a woman is not able to know about her husband cheating, she could even think that he is faithful... but all other 99 women know he is unfaithful. So, 100 groups of 99 women will charge each 100th woman's man, thus every woman will discover that his husband has betrayed her confidence... and she will have to kill him.

- ssr (11 Nov 2013)

Your answer is wrong, because you are giving the example with a fixed number, but the queen does not give a fixed number she gives a variable, ie "at least one" - which could be anywhere between 1 & 100.

To visualise this better imagine it's just 100 women (no husbands involved), and you are one of them - you all have a letter tattooed on your foreheads, "C" or "F" - there are no mirrors, no one has never seen their reflection, and no one can tell another person what their letter is.

If you have a C you have to commit Hari Kari.

If the Queen walks in and says "1 person has a C on their forehead" and you can see that everyone else has an "F" then you know it's you.

If the Queen walks in and says "2 people have a C on their forehead" you can see one other person has a C and everyone else an F, so you know it has to be you.

If she said "50 people have a C on their forehead" you can see the 49 C's, and the 50 F's, so you know that you are the 50th C.

But if she walks in and says "AT LEAST one person has a C on their forehead" - imagine their are 50 C's and 50 F's - you look around and see the 49 C's, so yes, the Queen is right.

But without knowing the exact number of C's (i.e. that there are 50) you cannot determine that you are the 50th, so you do not kill yourself since you still do not know which letter is tattooed on your forehead, and neither do the other 49.

The only way the "at least 1" results in someone killing themselves is when there are 99 F's and only 1 C, any more than that and everyone can see at least 1 C, and so cannot determine their own letter.

And so no one dies.
- Dave Shuttleworth (6 Feb 2014)

Dave, you're incorrect. Let's start where you did, with 1 person having a C and seeing everyone else with an F.

On the first day, the C knows it's herself.

Now let's say there are 2 women with a C. On the first day, nobody dies, because they know there is at least one other C. On the second day, though, after seeing that nobody died on day one, it means there must be two individuals with a C. If there was only one (the one they see), that person would know it, and have died. Because that didn't happen, on day two both people recognize they have a C.

And so on and so on, regardless of number. The queen only needs to mention 'at least 1 C' for this to work, with the number of days increasing for each additional C
- Danny (13 Jul 2014)

I think the statement "at least one husband cheated) makes the whole puzzle undetermined. Certainly, one man will be killed. But since we do not know if more than 1 man really cheated (can be anything from 1 to 100) the problem has no solution.
- Tony (11 Sep 2015)

Ssr is correct, if every man is unfaithful, aa the question states, all the wives will know 99 husbands other than their own have cheated.
- Spencrer (21 Oct 2016)