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Counting on Letters

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

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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

Label this plum tree graph to make it totally magic!

Cinema Problem

Stage: 3 and 4 Challenge Level: Challenge Level:1
What happens to the amount of money taken if an adult is replaced by a pensioner? Or a pensioner with a child? Or...?