### 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?

### Picture Story

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

### 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.

# Cubist Cuts

##### Age 11 to 14 Challenge Level:

A $3 \times 3 \times 3$ cube may be reduced to unit cubes ($1 \times1 \times1$ cubes) in six saw cuts if you go straight at it.

If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer? Answer the same question with a $4 \times 4 \times 4$ cube:

What about a cube of any size (an $n \times n \times n$ cube)?

This problem is taken from "Sums for Smart Kids" by Laurie Buxton, published by BEAM Education. To obtain a copy call the BEAM orderline on 020 7684 3330 quoting product code SMAR. (Price: £13.50 plus handling and delivery.)