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# Working Systematically

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### Shady Symmetry

### Pair Sums

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Mathematicians often talk about the importance of working systematically on a problem, rather than approaching it in a random, unstructured way. The tasks in this feature have been chosen because systematic approaches will offer the most efficient routes to the solutions.

Age 11 to 14

Challenge Level

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

Age 11 to 14

Challenge Level

How many different symmetrical shapes can you make by shading triangles or squares?

Age 11 to 14

Challenge Level

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?