The Putnam competition is a 6 hour, 12 question proof-based math test. Math majors, engineers, computer scientists, and physics majors are the ones who usually take it. The person with the highest score gets a scholarship to Harvard for graduate study in mathematics that covers tuition plus 12k. Archives:http://www.unl.edu/amc/a-activities/a7-problems/putnamindex....

Sample question: A1. Basketball star Shanille O'Keal's team statistician keeps track of the number, S(N), of successful free throws she has made in her first N attempts of the season. Early in the season, S(N) was less than 80% of N, but by the end of the season, S(N) was more than 80% of N. Was there necessarily a moment in between when S(N) was exactly 80% of N? (with proof) 168 out of the 196 top scorers got at least an 8/10 on this, so it was a relatively easy question for that year.