### Painting Cubes

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

### Tri-colour

Six points are arranged in space so that no three are collinear. How many line segments can be formed by joining the points in pairs?

### Permute It

Take the numbers 1, 2, 3, 4 and 5 and imagine them written down in every possible order to give 5 digit numbers. Find the sum of the resulting numbers.

# Paving Paths

##### Stage: 3 Challenge Level:

Well done Michael Brooker, age 9, home educated and Chris Waterhouse, Hethersett High School, Norfolk, for spotting the Fibonacci sequence here and finding that there are 89 different ways to lay the 10 paving slabs. Each slab is 2 foot by 1 foot and a path has to be made 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs. Chris drew all the different patterns for 1,2,3,4 and 5 slabs and you can try this for yourself. Here is Michael's solution: