Frequently, a logical step-by-step approach generates the solution to your problem.

Sometimes, you can make progress by thinking outside the box.

If all else fails, you can try the brute force approach for really tricky problems.

The idea is to list out all dimensions of your problem.

A dimension is some aspect about the problem.

For example, one aspect of a plumbing problem is the tool you’ll be using.

For each dimension, list out the discrete values it can take. In the case of the tool dimension in the plumbing problem, you could use a number of tools to loosen the bolt.

You’ve essentially got a bunch of lists for each dimension of your problem.

Compare each list with another list pair-wise. The idea is to examine each pair and judge whether they can exist together.

Exhaustively iterate and combine pairs from other dimensions. These pair combinations represent potential solutions to your problem.

If you’re stuck on a problem, this strategy is arguably the ultimate hammer to get you unstuck.

See the problem-solving checklist for more ideas about solving problems.