Yes you'd need to go through a lot of problems because every problem is slightly different
Realistically, it is rare that you would encounter hundreds of identical problems.
Take realistic examples: topcoder.com, Facebook's Hacker cup, and Google codejam. Or any university exam. Or SAT. Or Olympiam math. Their problems are unique because they can't just create the same problems over and over again.
There are also other aspects like solving the problems faster and being able to write up a solution correctly. Coding it correctly at the first try is really a magical moment.
Comments
Yes you'd need to go through a lot of problems because every problem is slightly different
Realistically, it is rare that you would encounter hundreds of identical problems.
Take realistic examples: topcoder.com, Facebook's Hacker cup, and Google codejam. Or any university exam. Or SAT. Or Olympiam math. Their problems are unique because they can't just create the same problems over and over again.
There are also other aspects like solving the problems faster and being able to write up a solution correctly. Coding it correctly at the first try is really a magical moment.