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Individual/Team Questions
1. Some students in a gym class are wearing blue jerseys, and the rest are wearing red jerseys.
There are exactly 25 ways to pick a team of three players that includes at least one player
wearing each color. Compute the number of students in the class.
2. Compute all real values of x such that log2(log2 x) = log4(log4 x).
3. Let k be the least common multiple of the numbers in the set S = {1, 2,…, 30}. Determine
the number of positive integer divisors of k that are divisible by exactly 28 of the numbers in
the set S.
4. Let N be a six-digit number formed by an arrangement of the digits 1, 2, 3, 4, 5. Compute the
smallest value of N that is divisible by 264.
5. Let A and B be digits from the set {0, 1, 2,….., 9}. Let r be the two-digit integer A B and let
s be the two-digit integer B A, so that r and s are members of the set {00, 01,….., 99}.
Compute the number of ordered pairs (A, B) such that r  s = k2 for some integer k.