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# One Reflection Implies Another

This problem builds on from 'A Roll of Patterned Paper'

#### For the unit shapes I've tried so far I noticed something
:

When a strip maps to itself with a mirror line somewhere across it,
there always seems to be a second place where a mirror line would
also map the pattern to itself.

An illustration may help :

The mirror could be at position 1 or at position 2, either way the reflection will map the pattern onto itself.

#### Your challenge :

Can you find a design with only one mirror line across the
strip?

Or perhaps, if you thought that was impossible, can you explain how you could be sure about that?

If you're ready for more, try the problem called 'Rotations Aren't Single Round Here'.

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Age 14 to 16

Challenge Level

This problem builds on from 'A Roll of Patterned Paper'

An illustration may help :

The mirror could be at position 1 or at position 2, either way the reflection will map the pattern onto itself.

Or perhaps, if you thought that was impossible, can you explain how you could be sure about that?

If you're ready for more, try the problem called 'Rotations Aren't Single Round Here'.

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?

The ten arcs forming the edges of the "holly leaf" are all arcs of circles of radius 1 cm. Find the length of the perimeter of the holly leaf and the area of its surface.