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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?

Counting Triangles

Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?

Combining Transformations

Age 11 to 14 Challenge Level:

This problem is the middle one of three related problems.
The first problem is Decoding Transformations and the follow-up problem is Simplifying Transformations .

We have adopted the convention of listing a sequence of transformations from left to right; teachers may want to mention to their students that in other contexts a sequence of transformations may be listed from right to left.