### 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.

### Network Trees

Explore some of the different types of network, and prove a result about network trees.

### Magic Caterpillars

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

# Limiting Probabilities

##### Age 16 to 18Challenge Level

The question requires an understanding of the definition of matrix multiplication and of the probability formulae $$p(u\ {\rm and}\ v) = p(u)\times p(v)$$ and $$p(u\ {\rm or}\ v) = p(u)+ p(v)$$
You will want to use a calculator (or software) that will work out matrix products for you.