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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?

Almost Total Inequality

Age 14 to 16
Challenge Level

Three expressions

When x is zero, A is greater than both B and C

For what other values of x is A the greatest ? (your answer will include that zero value of course)

For what x values is B the greatest ? And C ?

Is there a value of x when neither A or B or C is greater than the other two ?