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# Rotations Are Not Single Round Here

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

#### Your challenge :

#### Taking it further :

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Age 14 to 16

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.

Can you find a design with only one centre of rotation?

Or if you thought that was in fact impossible, could you say why that's true ?I noticed that if there are mirror lines across the strip, and if there is also a horizontal mirror line, then the strip always seems to have rotation symmetry.

Can that be explained?

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

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?

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?