### Burning Down

One night two candles were lit. Can you work out how long each candle was originally?

### Percentage Unchanged

If the base of a rectangle is increased by 10% and the area is unchanged, by what percentage is the width decreased by ?

### Digit Sum

What is the sum of all the digits in all the integers from one to one million?

# Adding a Square to a Cube

##### Age 14 to 16 ShortChallenge Level

Find all $9$ integer values of $n$ between $1$ and $100$ for which $n^2+n^3$ is a square number.

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