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Not Continued Fractions

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?

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Black and White Socks

Age 14 to 16 Short Challenge Level:

There are 20 black socks and $n$ white socks in a drawer.

When a sock is taken from the drawer, the probability that it is white is $\dfrac{1}{n}$.

What is the value of $n$?

This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.