# Thread: 40 people 40 nights ?

1. ## 40 people 40 nights ?

There was a puzzle up here about a year ago!
it was quite a long one and had something to do with a queen
and 40 people in a town, i can remember it being a good one
but cant remeber what the puzzle was ?

2. ## Re: 40 people 40 nights ?

by spooky coincidence i just found it by mistake

A Queen of an island kingdom was concerned about the high level of infidelity among the island's men, so she gathered all the married women of the island and made the following announcement:
"There is at least one unfaithful husband in our kingdom. All the wives know of all the unfaithful husbands, but know nothing about their own husband. You are not allowed to discuss your husband with any of the other women, but if it becomes known to you that your man is unfaithful, you must shoot him at midnight of the following night."

(Assume a shot anywhere on the island is heard at any other point on the island.)

After thirty nine nights of uneasy quiet, on the fortieth night the gunshots echoed across the island. How many men were shot that night, and why? (Assume the wives are all super smart.)

3. ## Re: 40 people 40 nights ?

Did we ever get an answer to this one? <img src=/S/confused.gif border=0 alt=confused width=15 height=20>

4. ## Re: 40 people 40 nights ?

Yes <img src=/S/exclamation.gif border=0 alt=exclamation width=15 height=15> Think about it ... (and no, I didn't get it the first time around)

5. ## Re: 40 people 40 nights ?

Did we get a detailed answer? I've been thinking about it and I arrived at this conclusion (simplified from 40 wives to 3).

With 3 wives, A, B and C, there are (from A's point of view) three combinations of faithful / unfaithful husbands, namely

1. <LI>Husband A, unknown, Husband B faithful, Husband C faithful
<LI>Husband A, unknown, Husband B faithful, Husband C unfaithful (or B and C the other way around)
<LI>Husband A, unknown, Husband B unfaithful, Husband C unfaithful
Under situation 1), A would know that her husband was unfaithful on night #1 and shoot him. That didn't happen, therefore situation 1) is not possible.

Under situation 2), A would assume that her husband was faithful and thus C would know that her husband was unfaithful on night #1 and shoot him. That didn't happen so A would deduce that her original assumption was wrong and she would shot her husband on night #2. That didn't happen, therefore situation 2) is not possible.

Under situation 3), A would assume that her husband was faithful. Furthermore, she would assumed that B assumes her husband is faithful and thus C would know that her husband was unfaithful on night #1 and shoot him. That didn't happen so B's assumption was wrong and that she ([img]/forums/images/smilies/cool.gif[/img] would shot her husband on night #2. Now that didn't happen, so A's original assumption was wrong and she would shot her husband on night #3.

Similar to A, B and C would also go through this process and shoot their husbands on night #3.

So, by extension, with 40 wives and husbands, all 40 husbands would be shot on night #40.

6. ## Re: 40 people 40 nights ?

I got the same answer just by assuming this was one of those "all men are unfaithful pigs" ideas: all the men would be fooling around (because that's what "all men do, ain't it") so - bang! - the girls would off them all.

Although I think the key point of "All the wives know of all the unfaithful husbands, but know nothing about their own husband." means no one is: if all the wives knew all the unfaithful husbands, then the wife of the unfaithful husband would have to know her husband was unfaithful - otherwise, she wouldn't know he was unfaithful and hence wouldn't know all the unfaithful husbands. That's a contradiction: she's a wife, she knows about all unfaithful husbands yet not her own, so her own can't be unfaithful, hence no man is unfaithful.

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