### Coke Machine

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design. Coins inserted into the machine slide down a chute into the machine and a drink is duly released. How many more revolutions does the foreign coin make over the 50 pence piece going down the chute? N.B. A 50 pence piece is a 7 sided polygon ABCDEFG with rounded edges, obtained by replacing AB with arc centred at E and radius EA; replacing BC with arc centred at F radius FB ...etc..

### Get Cross

A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?

### Illusion

A security camera, taking pictures each half a second, films a cyclist going by. In the film, the cyclist appears to go forward while the wheels appear to go backwards. Why?

# Rotations Are Not Single Round Here

##### Stage: 4 Challenge Level:

If you haven't seen the problem 'A Roll of Patterned Paper' you may want to try that first.

In that problem I'd been finding designs for streamers - this problem follows on from that.

#### I noticed this about the streamers that had rotation symmetry :

In the ones I tried, if there was one centre of rotation there always seems to be another centre that worked as well.