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Check Code Sensitivity
Age 14 to 16
Challenge Level 
Remember that to show that a result is not true, or that a method
fails, you only have to find one counterexample, that is one case
where it fails. To prove that a result is always true you need a
completely general argument. No matter how many cases you give
where the result is true that does not prove that it is
always true.
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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.