### 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?

# Making Rectangles, Making Squares

##### Stage: 3 Challenge Level:

Imagine you have any number of equilateral triangles all of the same size as well as a large number of $30$ $^\circ$ , $30$ $^\circ$ , $120$ $^\circ$ isosceles triangles with the shorter sides the same length as the equilateral triangles.

Using these triangles how many differently shaped rectangles can you build?

Can you make a square?

The interactivity below may help you with this problem. Click on the green or yellow triangles to get a copy. Drag the triangle by its interior to the required position and drag any vertex to rotate it.

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