Book recommendation for Putnam/Olympiads

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I have been concentrating on olympiad questions, and PUTNAM exams, Putnam is my main focus. Can you suggest a book from one of these:

  1. Problem Solving Strategies By Arthur Engel
  2. Putnam and Beyond by Andreescu Titu et. al

First, can you tell me which one is better from the above? I only have one choice?

Any other book recommendations is greatly appreciated!

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How could you do better than the problems and solutions themselves for past Putnam exams?

  1. 1938-1964
  2. 1965-1984
  3. 1985-2000

For a Putnam archive of past exam questions and solutions, check out this website maintained by Kiran Kedlaya.

There are, of course, many other resources, but these are by far the best I know to date.