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Cushion Ball

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

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This is a beautiful result involving a parabola and parallels.

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Square Pair Circles

Investigate the number of points with integer coordinates on circles with centres at the origin for which the square of the radius is a power of 5.

Napoleon's Hat

Age 16 to 18 Challenge Level:
One possibility is to use coordinates. You need to use the coordinatesof the centroids of the triangles.