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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?

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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.

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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?

Matching Frieze Patterns

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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.