### All in the Mind

Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?

### Instant Insanity

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

### Is There a Theorem?

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

# Paving Paths

##### Age 11 to 14Challenge 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: