### 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.

# Olympic Magic

##### Age 14 to 16Challenge Level
The Olympic emblem consists of five coloured rings which overlap to give nine regions. Here is a black and white diagram showing the overlaps:

In order to contribute to a pension fund for the retiring International Olympic Committee people are asked to deposit money into each region.
The guidelines allow the delegate to take all the money in any one of the rings.

Place the numbers 1, 2, ... 9 in the nine regions so that the amount in each ring is the same. How many different ways can you find to do this?
(Problem from University of Sydney Mathematics Enrichment Groups 1999)