Putnam exam preparation?

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I'm part of the math club at my college. Recently the professor who runs the club a mock Putnam exam using the same test format (two three hour sessions) with problems recycled from old tests. I didn't know exactly what I was walking into since by an odd coincidence "Putnam" also happens to be the name of a large-ish town near where my school is and I thought he was just playing off that, but anyway I ended up getting two full solutions and a partial solution for a third, so now they've talked me into taking the real thing this December.

How would one go about preparing? I've only been in anything even resembling a math competition once (SkillsUSA applied technical math), and that was years ago (although, I did win second in state for that one, for whatever it would be worth). And I'm not a math student, my major is electrical engineering with a physics minor, is it open to non-math majors?

Any advice at all would be nice...I have a year to get ready.
 

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