Problem-solvers vs. Problem-solved-ers

I wish people talk more about the difference between a problem-solver and a problem-solved-er.

The latter is a person whose sole motive is to get rid of problems at all costs. You would find such a person agonizes at every step and every second during the actual problem solving process. Never for a second he would marvel at the odd idea of "problems are fun as they challenge you and push your limits". "Equating the word 'problems' with 'fun'? You can't be any more lunatic!", he said. 

The former, while caring about getting a problem solved at the very end (because otherwise he is just a lazy-bum who never gets anything done), derives equal amount of (if not more) delight from the apparently gnawing problem on his hand. 

For a problem-solved-er, the sole reason to bend over backwards is the final reward of "problem solved". Anything before that is excruciating evil.

For a problem-solver, the struggle during the problem-solving process is by itself the real reward, while the destination of "problem solved" is merely a checkpoint, like how the 90-th minute mark is a reminder to a professional soccer player that "Let's take a break and continue again next week".

At the extreme case, he even wishes that the problem on his hand would last longer, that he wouldn't be able to have it solved so quickly, because solving it signifies the end of the fun part of problem-solving.