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Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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Some(?) of the Parts

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

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Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

Red or Black

Stage: 3 and 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

CubeEach edge of the cube borders borders two faces. As there are six faces, a minimum of three black edges will be required.

The diagram on the right shows that three black edges is enough.


This problem is taken from the UKMT Mathematical Challenges.
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