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Building Tetrahedra

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

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Ladder and Cube

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

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Bendy Quad

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

Always Perfect

Age 14 to 16 Challenge Level:

There are a variety of ways of proving this. Looking at products rather than factors may be easier.

The factorisation can be done by inspection using the first and last terms, as in the second hint.

An opportunity to discuss the representation of consecutive numbers, consecutive even numbers, odd numbers, numbers that are divisible by three etc.