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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 Short
Challenge 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.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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