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396
Age 14 to 16
Challenge Level 
The four digits 5, 6, 7 and 8 are put at random in the spaces of the number below:
3 _ 1 _ 4 _ 0 _ 9 2
- Estimate the probability that the answer will be a multiple of 396.
- Calculate the probability and explain your answer.
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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.