Rudin vs Courant for 'contest-like' problems. For contests like, say, Putnam, would Rudin's _Principles_ or Courant's _Calculus_ be a better fit? Courant's book has a lot more problems, and the mathematics involved much more closely resembles what's there is contest calculus. On the other hand, the problems seem mostly trivial or bruteforce computation-based. I am entirely sure that is not true of Rudin. Please help.

If you want Putnam Style problems a putnam book may be better suited. Have you looked at Problem Solving through Problems (Larson) or Putnam and Beyond?