### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

# London Eye

##### Stage: 3 and 4 Short Challenge Level:

Each spoke of the London eye is about $\frac{1}{20}$ mile long. As 1 mile is approximately 1600m this means that the radius of the giant wheel is roughly 80m. So the circumference is approximately 500m.

This problem is taken from the UKMT Mathematical Challenges.
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