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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.

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Magic Caterpillars

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

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Plum Tree

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Olympic Magic

Age 14 to 16 Challenge Level:

The Olympic emblem consists of five overlapping rings containing nine regions. 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)
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