Infidelity
by Kevin J. Lin
Seven men had been done in in their sleep- one for each night.
The logic to unravel this is quite similar to the logic behind the Three
Hats. Consider what would happen if there had been only one unfaithful
man. Every woman in town would immediately know, except that man's wife.
But if you were that woman, wouldn't you quickly wonder why no gossip
hound had informed of this fact? Of course you would- then it would dawn
on you and CHOP! (or bang, or zap, or whatever) he's dead.
On day two, when there's no corpse, what would all the women think? "Aha!
There's more than one philanderer in this town."
If there were exactly two unfaithful men in town, both their wives would
only know about the other's infidelity. Combine this with the fact that
they know there is more than one, "If there's two philanderers in
this town, and I only know of one, and the only way I wouldn't know of
the other is if he were..." Kablam!
And so it progresses. The wives of the faithful men believe (correctly)
there to be as many unfaithful men as they know about, and no more. The
wives of the unfaithful men (incorrectly) believe the same. As each night
passes without a murder, the minimum number of cheaters rises by one.
As it happened, six nights passed uneventfully, meaning that there were
at least six unfaithful husbands. The seven women who only knew about
six spend that day buying their poisons, loading their weapons, sharpening
their daggers and whatnot. And that night, The End.