The Surprise Examination

This paradox is so famous that I nearly left it out. It raises some intriguing issues.

Teacher tells the class that there will be a test one day next week (Monday to Friday), and that it will be a surprise. This seems reasonable: the teacher can choose any day out of five, and there is no way that the students can know which day it will be. But, the students don’t see things that way at all. They reason that the test can’t be on Friday —- because if it was, then as soon as Thursday passed without a test, they’d know it had to be Friday, so no surprise. And, once they have ruled out Friday, they apply the same reasoning to the remaining four days of the week, so the test can’t be on Thursday, either. In which case, it can’t be on Wednesday, so it can’t be on Tuesday, so it can’t be on Monday. Apparently, no surprise test is possible.

That’s all very well, but if the teacher decides to set the test on Wednesday, there seems to be no way that the students could actually know the day ahead of time! Is this a genuine paradox or not?

Reference: Professor Ian Stewart’s Cabinet of Mathematical Curiosities.

Thanks for Prof Stewart for entertaining us! 🙂

More later,

Nalin Pithwa

One Comment

1. Anubhav Clancy Singh