### Just Rolling Round

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

### Coke Machine

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

### Just Opposite

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?

# Steel Cables

##### Age 14 to 16Challenge Level

Do you know a quick way of adding up all the numbers from 1 to n?
If not, take a look at the problem Picturing Triangle Numbers.

Below are student diagrams from the problem page, but they now also show the working that the students used to explain their diagrams. Can you explain their reasoning?

Group 1

Group 2

Group 3

Group 4

If you are finding it difficult to make sense of the different groups' work, try to work out what they might have drawn for a size 6 cable.