Riddle: Island Adultery
100 married couples live on a remote island. There is a law on the island that states that if a man finds out that his wife is unfaithful, he must kill her that night and leave her body at the center of the island for everyone else to see.
It turns out that all one hundred wives are cheating on their husbands. No husband knows that his own wife is unfaithful, but every husband knows that every OTHER wife is a cheater. The fact that each husband knows about every wife except his own is common knowledge to everyone.
One day, an oracle arrives on the island and announced to everyone: "At least one of the woman on the island is a cheater." Everyone knows that the oracle only speaks the truth.
Assuming every man on the island is, and is known to be, a perfect logician, what happens next?