The answer is one: the guy who spent most of his time honing his skill, and mastering his domain.
It's that simple.
No one can solve a problem unless he/she knows the problem inside out and has the pieces to solve the problem (a.k.a previous experience: success or failure).
You can't put someone who is not familiar with the problem domain and expect him to do superb job given a deadline. If he can solve it under-pressure and on-time, chances that he has previous experiences or building blocks that can help him greatly.
The problem with most people is that they're focusing on the wrong thing because of many reasons: distraction from family, distraction from the things they read, tend to spend too much time viewing the problem from the same perspective instead of taking some time off to think about it from a different angle.