### 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?

# Fibonacci Deduction

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

If we let the fifth number be $x$, then the sixth number is $6+x= 15$, so $x=9$.

The seventh number is the sum of the fifth and sixth numbers, $9+15=24$.

This problem is taken from the UKMT Mathematical Challenges.
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