### 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?

# Alphabetical Angle

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

There are 24 arrangements of the letters in the word ANGLE with A as the first letter (the number of ways of arranging the other 4 letters is $4\times3\times2\times1$). In alphabetical order AEGLN is first and ANLGE is last. ANLEG is the 23rd and hence ANGLE is in the 22nd position on the list.

This problem is taken from the UKMT Mathematical Challenges.
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