Surprise exam paradox

Martin McBride
Graphic maths
Published in
6 min readJun 17, 2024

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Photo by Joshua Hoehne on Unsplash

The surprise exam paradox is a paradox that relates to our knowledge of future events. It is also known as the unexpected hanging paradox if you prefer a more macabre scenario.

It was first popularised by the maths and science writer Martin Gardener in the 1960s, in his excellent Mathematical Games column in Scientific American magazine. The paradox was originally proposed by mathematician Lennart Ekbom in the 1940s.

To date, there is no generally accepted resolution to the paradox. We will look at a few of the popular attempts at solutions here.

The paradox

A maths teacher tells her class that she will be setting an exam in the next week, but that the exam will be a surprise to them. They won’t know what day the exam will be until they arrive in the class and she hands out the paper.

The class, who are all grade A students, discuss the situation and conclude that there will be no exam.

Their reasoning is as follows. The exam couldn’t be on Friday, because on Thursday evening, if they hadn’t already had the exam, they would know the exam was going to happen on Friday. That would contradict the teacher’s assertion that the exam would be a surprise.

But the exam couldn’t be on the Thursday either. On Wednesday evening, if they hadn’t already had…

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