I am offerring training to students in Years 5 - 10 who are interested in entering mathematics competitions. Typical questions that will be attempted include (obtained from internet resources):

(1) Find a formula that generates the series 3, 6, 9, -6,......

(2) Find the number that (a) is the product of two primes and (b) has 2014 as the sum of its proper divisors

(3) Suppose we have a single line queue consisting of a random number of males and females. Prove that it is always possible, for any queue length, to insert yourself into the queue such that the number of females behind you equals the number of males in front of you.

(4) Consider the number m = x(x+1)^2 (x+2)^3 (x+3)^4 obtained from any positive integer x. Find the largest positive integer that is always a factor of m for all values of x.