### 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?

# Platinum Puzzle

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

Platinum is a very rare metal, even rarer than gold. Its density is $21.5\textrm{ g/cm}^3$. Assuming that the world production has been about $110$ tonnes for each of the past $50$ years, and negligible before that, which of the following has a comparable volume to that of the total amount of platinum ever produced?

A: a shoe box, B: a cupboard, C: a house, D: Buckingham Palace, E: the grand Canyon

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

This problem is taken from the UKMT Mathematical Challenges.
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