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Finding Factors
Age 14 to 16
Challenge Level 
What does the constant term of the quadratic expression tell you
about the headers?
What does the coefficient of x tell you about the headers?
What does the coefficient of x tell you about the headers?
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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.]
Common Divisor
Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
Novemberish
a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.