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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!

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Olympic Magic

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

The Great Weights Puzzle

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This problem follows on from 9 Weights

You have twelve weights, one of which is heavier or lighter than the rest, but you don't know which one is heavier or lighter. Using just 3 weighings on the balance, can you identify which weight is the odd one out, and whether it is heavier or lighter?


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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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