I have been concentrating on olympiad questions, and PUTNAM exams, Putnam is my main focus. Can you suggest a book from one of these:
First, can you tell me which one is better from the above? I only have one choice?
Any other book recommendations is greatly appreciated!
How could you do better than the problems and solutions themselves for past Putnam exams?
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.