### 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?

# Truncated Tetrahedron

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

At each vertex, the piece that has been removed is a regular tetrahedron. Three of the edges of this are the pieces of edge that are lost from the original tetrahedron, the other three are the new edges of the truncated tetrahedron. Since all the edges are the same length, this means the total length of the edges remains unchanged.

Therefore, the total length of the edges is $6\text{cm} \times 6 = 36\text{cm}$.

This problem is taken from the UKMT Mathematical Challenges.
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