## 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

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## One Comment

The Friday part might be accurate, as a test held on a Friday will not be a surprise; but unfortunately Friday is still a part of the calendar and thus cannot be excluded. Therefore a test on Thursday will still be a surprise, though not that surprising. Because, assuming the test to be on Thursday, at the end of Wednesday you can still say that the test might be on Thursday or Friday. My theorem is you cannot judge a test to be a surprise test or not UNTIL it happens. The students raise a fair point though, wish that could be true for all MY tests. 😛