One of the most useful problem solving heuristics I’ve come across is this one: If you can’t solve the problem you’re working, you’re working on the wrong problem.
The “normal” approach to problem solving is to assume that you are either capable or incapable of solving a problem. When confronted with the problem you jump right in. If you can’t solve it, you conclude that you’re not capable of solving the problem. So you go away angry or depressed. We are trained to think this way early on, in school, where problems are often presented in a can-solve/cannot-solve dichotomy. But real problems are not so. They don’t go away even when we do. And the ones worth solving are more than worth the sweat. What this heuristic says is that if you find nothing working, then re-approach the situation from a different angle, one you feel more likely to have success with. Keep pivoting this way until you get an angle that you can work with.
This approach takes the personal investment out of problem solving–it’s no longer about do or die, but about finding the right problem for where you are right now.