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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?

Matching Frieze Patterns

Age 11 to 14 Challenge Level:

Each frieze pattern is formed by repeating copies of one small bit of the pattern (the motif) over and over again by translation, rotation and reflection. Sort the frieze patterns into seven pairs according to the way in which the motif is repeated. Explain how you match the pairs.