### 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.

### Ladder and Cube

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?

# 2011 Digits

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

$20 \div 11 = 1\frac{9}{11} = 1.81818181...$. So the first 2011 digits are 1006 '1's and 1005 '8's. Therefore the required total is $1006\times1 + 1005\times8 = 1006 + 8040 = 9046$.

This problem is taken from the UKMT Mathematical Challenges.
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