### 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?

# Poly-puzzle

##### Stage: 3 Challenge Level:
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This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

Can you cut up any triangle, using straight cuts, and rearrange the pieces to make a rectangle and a square?
Start by just investigating triangles which have a height of less than twice the base but greater than half the base. Make your own puzzle from card by cutting the triangle into a small number of pieces that can be re-arranged into a rectangle and into a square with the same area.

Suppose you have two triangles with the same area. Do you think you can cut one into pieces which can be re-arranged to form the other?