### 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?

# Pile Driver

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

The diagram shows a figure made from six equal, touching squares arranged with a vertical line of symmetry. A straight line is drawn through the bottom corner $P$ in such a way that that the area of the figure is halved.

Where will the cut cross the edge $XY$?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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