Complementary Counting
AMC 8 LEVEL PROBLEMS
I know, you know, everyone knows. "when the question says 'not' or 'at least', use complimentary counting". The reality is a lot more complicated and interesting. Realizing when complementary counting can make the problem simpler is the challenge.
1987 AJHSME Problem 25 (note that there is only one way to get an odd sum - where the two numbers must be of opposite parity - making the complementary approach more efficient).
AIME LEVEL PROBLEMS