I absolutely agree with GrandFather++.

Programmers more than anything else are problem solvers

I couldn't agree more.

The following is the very beginning of Chapter 1 of my coming book on programming in Perl 6, Think Perl 6 - How to think like a computer scientist (see New Perl 6 book coming out with O'Reilly), although, to tell the truth, this particular passage was not originally written by me, but my co-author, Allen B. Downey:

The goal of this book is to teach you to think like a computer scientist. This way of thinking combines some of the best features of mathematics, engineering, and natural science. Like mathematicians, computer scientists use formal languages to denote ideas (specifically computations). Like engineers, they design things, assembling components into systems and evaluating tradeoffs among alternatives. Like scientists, they observe the behavior of complex systems, form hypotheses, and test predictions.

The single most important skill for a computer scientist is problem solving. Problem solving means the ability to formulate problems, think creatively about solutions, and express a solution clearly and accurately. As it turns out, the process of learning to program is an excellent opportunity to practice problem-solving skills. (Emphasis in the original.)