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?
Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?
Is the mean of the squares of two numbers greater than, or less than, the square of their means?