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# Almost Total Inequality

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

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### Two Cubes

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Age 14 to 16

Challenge Level

- Problem

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 ?

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?