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.

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.