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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.]

Rationals Between...

What fractions can you find between the square roots of 65 and 67?

Square Mean

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


Age 14 to 16
Challenge Level

Tet-trouble printable sheet

tetrahedraIs it possible 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?