Kai-Chen

The Pigeonhole Principle is one of the simplest uses of syllogism, simple enough to be understood by a 4th grader.
But its simplicity is lost in a formal definition.
So its usefulness is best appreciated through an example, especially an example that can lead to true yet unexpected results.

For example, given that:
1) At the trial of Socrates, Athenians found him guilty by a vote of 280-220
2) The same set of jurors sentenced Socrates to die by a vote of 360-140
one may conclude that:
3) because more jurors sentenced Socrates to die than found him guilty, there must be some (at least 80) jurors who condemned Socrates to die while believing him to be innocent.