144 // The Surprise Examination

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've 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?

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Answer on page 281

Antigravity Cone In defiance of the Law of Gravity, this double cone rolls uphill. Here's how to make it.

Five pieces

to cut out.

two page view?

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