A programmer who knows how each line of his code really works, can crack a bug by simply reading over the code he wrote.
A doctor who knows how a wound is formed, can heal it in weeks.
A bowler who knows how reverse swing really works, can produce it at will. (okay he may need some luck too:))
I'm guessing, life, works pretty much the same way; if you are strong on the fundamentals, there probably is no unsolvable problem.