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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.


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

These patterns are Japanese, but frieze patterns occur in many cultures. The article Frieze Patterns in Cast Iron also illustrates all seven types of frieze patterns.

See the article The Frieze Tree for a discussion of why there are only seven possible types of frieze pattern.