### 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?

# Sticky Fingers

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

Any three positive integers that multiply to make $2009$ would create viable cuboids.

The prime factors of $2009$ are $7\times 7\times 41$, so the options are:
$1 \times1 \times 2009$
$1\times 7\times 287$
$1\times 41\times 49$
$7\times 7 \times 41$

The first three cuboids all have two faces which each require $2009$ stickers ($1\times2009$, $7\times287$ and $41\times49$ respectively) so Roo cannot cover them.

The last cuboid has surface area: $2\times( 7\times7+7\times41 + 41\times 7) = 1246$

This leaves $2009-1246=763$ stickers left over.

This problem is taken from the UKMT Mathematical Challenges.
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