In a small town there are N married couples in which one of the pair has committed adultery. Each adulterer has succeeded in keeping their dalliance a secret from their spouse. Since it is a small town, everyone knows about everyone else's infidelity. In other words, each spouse of an adulterer thinks there are N - 1 adulterers, but everyone else thinks there are N adulterers.

People of this town have a tradition of denouncing their spouse in church if they are guilty of adultery. So far, of course, no one has been denounced. In addition, people of this town are all amateur logicians of sorts, and can be expected to figure out the implications of anything they know.

A priest has heard the confession of all the people in the town, and is troubled by the state of moral turpitude. He cannot break the confessional, but knowing of his flock's logical turn of mind, he hits upon a plan to do God's work. He announces in Mass one Sunday that there is adultery in the town.

Is the priest correct? Will this result in every adulterer being denounced?

Priest Solution

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