Teach the Pigeonhole Principle using the example of the trial of Socrates

socrates-pigeonhole.txt

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.

This is a good example to teach and illustrate Pigeonhole because the conclusion is shocking enough to make the student want to go through the logic at least one more time, and yet not so shocking as to hijack the train of thought.

It still, probably, isn't effective enough with children between the age of 9 and 13.

[First posted on https://www.linkedin.com/pulse/socrates-pigeonhole-principle-sean-kai-chen/]