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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?


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

Turn the triangle of area 0.5bh into a rectangle of dimensions b by 0.5h using the midpoints of edges. The square has side length given by s2 = 0.5bh. There is a lot to explain here about why the pieces fit exactly as shown.