### Chess

What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?

### 2001 Spatial Oddity

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.

### Screwed-up

A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?

# Simplifying Transformations

##### Stage: 3 Challenge Level:

This is a hint to help you show that you've found all of the different transformations:

Once you think you've found them all, try drawing the upside-down `L' shape on a piece of squared paper, and draw the effects of all of the different transformations on that shape on the same piece of squared paper.
What happens if you apply $R$ or $S$ to one of the shapes now? How does this help you?

If you need some squared paper you can download it here .