> Is it just applying past experiences to a new situation, or can you learn to look for solutions?

You can achieve anything you put your mind to. It took me a while to realize this. Turns out the brain is a marvelous machine and once it has a goal (solve such and such a problem) it will try everything in its power to solve it, since it's a goal-oriented machine. People doubt their own capabilities, and don't believe in themselves, which is their own downfall.