At one extreme is the weekly sudoku puzzle that is completed for my own enjoyment and I am content with my mastery level. At that extreme I pick A, it is not really a goal to improve my sudoku skill, negative results contribute little.

At the other extreme are your hard coding problems, complex engineering problems, and those little bent steel puzzles that you have to take apart and reassemble in apparently impossible ways; Here the long term goal is not to solve the single problem but to learn and solve the problem type. These problems are either without an A solution, or you want greater mastery of the field so that next time only A or B solutions are on the table instead of the B and C solutions. Eventually your peers start coming to you with their A, B, C dilemmas and you can give them the right answer with 100% confidence. After that you will be known as a guru in your field and reap all the prestige and profit that comes with that (results may vary depending on field).

In short it depends on your goal, A to solve the problem, C to solve the problem type. B is a compromise if you want C but the budget doesn't allow for it.