seasong said:
During a particularly troubled time, the queen became troubled by the constant rumors of infidelity by husbands. Everyone knew who was being unfaithful... except the wives.
Thirty-nine silent nights followed the queen's announcement. On the fortieth night, shots were heard.
How many unfaithful husbands were there, and how did the women know? [/B]
I have cut it down to the bare minimum.
Let us assume you are the wife of an unfaithful husband.
You know about every unfaithful husband except your own.
That means you know about (N-1) unfaithful husbands where N is the total number of
unfaithful husbands.
You know there is at least one unfaithful husband.
Therefore, if you know of no unfaithful husband (i.e., yours is the only one), you would immediately deduce that he is the one and kill him that first night.
If there were no shots the first night, that indicates that EVERY wife knows of at least one unfaithful husband, so the number of unfaithful husbands must be greater than one.
Thus, if there are no shots on the first night, you know there are at least two unfaithful husbands. If you only know of one, your husband is, by default, #2. You shoot him. (incidentally, so does the other wife - 2 shots).
If there are no shots the first two nights, you know there are at least three unfaithful husbands. If you know of only two, your husband is, by default, #3. You shoot him (so do the other two, having arrived at the same conclusion
- 3 shots).
Repeat ad nauseum. Thus, you go until N wives (the number with unfaithful husbands) realize that they all have unfaithful husbands, as N-1 nights went by without any shooting and they only know of N-1 unfaithful men.
Thus the answer is 40 - and the women who knew of 39 unfaithful husbands were the ones who executed their husbands (the women who knew of 40 unfaithful husbands then knew their husbands were faithful).
--The Sigil
Edit - fixed a typo (put faithful where I should have put unfaithful) and added the not about 3 shots. Edits are in italics.
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