For programmers, then, we can define problem solving as writing an original program that performs a particular set of tasks and meets all stated constraints.

When faced with an onerous problem, I experiment with a reduced version of the problem. These experiments frequently produce valuable insights.

Planning also allows you to set intermediate goals and achieve them. Without a plan, you have only one goal: solve the whole problem.

In essence, most programming books for beginners teach how to read a program, not how to write one.

The broader lesson is that thinking about the problem may be as productive, or in some cases more productive, than thinking about the solution. In many cases, the correct approach to the solution is the solution.

The chief lesson here is the importance of recognizing analogies. Here, we can see that the Quarrasi lock problem is analogous to the fox, goose, and corn problem. If we discover that analogy early enough, we can avoid most of the work of the problem by translating our solution from the first problem rather than creating a new solution.

Problems include constraints, unbreakable rules about the problem or the way in which the problem must be solved.

It’s better to develop a strategy than to attack the problem through trial and error.

In many cases, the correct approach to the solution is the solution.

When solving problems, working with a specific goal in mind is always better than random effort, whether you achieve that specific goal or not.