V.Anton Spraul

Make no mistake: Programming, and especially problem solving, is a creative activity. Creativity is mysterious, and no one can say exactly how the creative mind functions.

When faced with an onerous problem, I experiment with a reduced version of the problem.

The other lesson is that sometimes problems are divisible in ways that are not immediately obvious.

Even if you are unable to find a clean division, you may learn something about the problem that helps you to solve it. When solving problems, working with a specific goal in mind is always better than random effort, whether you achieve that specific goal or not.

Restating the problem in a more formal manner is a great technique for gaining insight into a problem.

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 main lesson from sudoku is that we should look for the most constrained part of the problem. While constraints are often what make a problem difficult to begin with (remember the fox, the goose, and the corn), they may also simplify our thinking about the solution because they eliminate choices.

This is perhaps the most important rule. You must always have a plan, rather than engaging in directionless activity.

General Dwight D. Eisenhower was famous for saying, “I have always found that plans are useless, but planning is indispensable.”

the Prussian Helmuth von Moltke, famously said that “no plan survives first contact with the enemy”). But no army can succeed without planning and organization. Through planning, a general learns what his army’s capabilities are, how the different parts of the army work together, and so on.