Usually between 2,000 and 3,000 students enter the competition each year. The prizes for the top finishers include cash money, mathey fame, and a full graduate scholarship to Harvard University. If you're anywhere near the top (say you're in the top ten percent) you'll be getting offers from universities and technical institutes all over the place. School teams compete for glory and pats on the back. You think Who Wants To Be A Millionaire? is exciting stuff? Peh, you've never experienced the pure Putnam joy running through your veins.
If you've ever seen the kind of questions on the International Math Olympiad, then you have an idea what the Putnam examination is like, but using a bit more advanced math. You really ought to know the bare basics of calculus (including differential equations,) complex analysis, linear algebra, geometery, number theory, probability and combinatorics, and, well.... nothing will hurt you to know, really. Being clever will serve you a least as well as being knowledgeable.
No calculators or computers, of course (not that they'd help much anyway.) It has twelve questions (though some may have multiple parts) and is administered in two sessions, each three hours long. You can score from 0 to 10 points on each question, so theoretically you could score 120.
I should point out, though, that year after year the average score is less than one point. Oh yes, you can have your butt kicked so many ways by the Putnam math exam. It utterly rocks. (Have I made this sound cool yet?)
Below, you can find some example problems from the tests to practice on. I've provided solutions for them, but you might not want to look at those until you've actually tried the problems yourself. (I think that in most cases I've provided a reasonably elegant solution, although there are a couple questions that I really think can be answered easier.)
People competing in athletic competitions run their poor young bodies into the dirt with strenuous exercises (and sometimes, illegal chemicals.) Well, whoopty-dink. Play it safe and "beef up" your brain instead of your body. You'll burn a ton of calories just from the thinking!
So if you have any interest in math problems and puzzles, and have a good knowledge of undergrad mathematics, then you'll probably enjoy working through these a lot.
Oh, but if you're a confirmed mathophobe, stay FAR AWAY. VERY FAR AWAY.
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