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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.]
What fractions can you find between the square roots of 65 and 67?
Is the mean of the squares of two numbers greater than, or less than, the square of their means?
Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?