### Latin Numbers

Can you create a Latin Square from multiples of a six digit number?

### Hypotenuse Lattice Points

The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

### Big Powers

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

# 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.