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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.

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Tree Graphs

A connected graph is a graph in which we can get from any vertex to any other by travelling along the edges. A tree is a connected graph with no closed circuits (or loops. Prove that every tree has exactly one more vertex than it has edges.

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Magic Caterpillars

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

Cube Net

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

The use of set terminology here should not hold anyone up as they can find the definition in the Thesaurus. This is an exercise in combinatorics and it also gives a method for solving the problem about the sequence of subsets.