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Three monkeys met for tea in their favourite cafe, taking off their hats as they arrived.
When they left, they each put on one of the hats at random.
What is the probability that none of them left wearing the same hat as when they arrived?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.