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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.

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.

Magic W

Age 14 to 16
Challenge Level
Even though this subject is accessible to school students, Magic Graphs is currently an active research field (see Joseph Gallian's website which lists all the papers published on the subject).