Pop Quiz Paradox

When my kids were small, I would tell them about famous philosophical or mathematical paradoxes.

Yablo’s paradox didn’t really resonate with any of them, and various sorites paradoxes mainly got a “so what?”

But the Seven Bridges of Koenigsberg and the Surprise Examination Paradox got a lot of play.

One of my kids was in second or third grade when I told her about the Seven Bridges of Koenigsberg. I had printed some paper diagram of islands and rivers in the proper arrangement. She said, “Don’t tell, I’m going to figure this one out on my own.” She did not figure it out on her own.

The paradox that got the most traction was the Surprise Examination Paradox, or as I phrased it, the Pop Quiz Paradox.

Some Friday, your teacher announces that there will be a pop quiz next week. You won’t be able to know when the pop quiz will happen until the teacher puts the quiz on your desk.

That means the quiz won’t happen on Friday, because if the quiz doesn’t happen on Thursday, you’ll know it will happen on Friday, and the teacher said you won’t know when it will happen.

Since the quiz won’t happen on Friday the quiz won’t happen on Thursday, because if the quiz doesn’t happen on Wednesday, you’ll know it happens on Thursday, and again your teacher said you won’t know when the quiz will happen.

You can follow this procedure until you know the quiz won’t happen on Monday, either. The quiz won’t happen at all.

Everything was great until one of my kids came home one day and told me that the Pop Quiz Paradox wasn’t true. The teacher told her class that a surprise quiz would happen, and it actually did happen.

You might think this is all just playing Confuse-A-Kid, but I do get Ship of Theseus memes from my kids, and one of my kids got me a utility graph coffee mug for Christmas one year.