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Two Cubes

Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to prove you have found all possible solutions.]

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Rationals Between

What fractions can you find between the square roots of 56 and 58?

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Square Mean

Is the mean of the squares of two numbers greater than, or less than, the square of their means?

Tet-trouble

Stage: 4 Challenge Level: Challenge Level:1

tetrahedra

Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units.

Is it possible for a tetrahedron to have edges of lengths 10, 20, 25, 45, 50 and 60 units?

Can you write a set of general rules for someone else to use to check whether a given six lengths could form the edges of a tetrahedron?