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# Last-but-one

##### Age 14 to 16 ShortChallenge Level

If all the integers from $1$ up to $n$ are multiplied together, this is called the factorial of $n$, and is written as $n!$.

For example, $4! = 4 \times 3 \times 2 \times 1 = 24$.

This means that the last-but-one digit of $4!$ is $2$.

What is the last-but-one digit of $99!$?

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.