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# Two Cubes

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### Square Mean

### Not Continued Fractions

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Age 14 to 16

Challenge Level

- Problem
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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.]

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?