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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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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?

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Poly-puzzle

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

Chess

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

Place a Knight from a chess set on the corner of a 3 by 3 square board:




It would need 4 usual Knight's moves to place it in the opposite corner. One possible set of moves is shown below:




  • What would be the smallest number of moves needed to move from one corner to the opposite corner of a 99 by 99 square board?

  • What would be the smallest number of moves needed to move from one corner to the opposite corner of an n by n square grid?