Problem solving techniques often deal with understanding and attacking the problem, and how to do so in the most effective and least risky way.
All of this is useful, and I don't want to under-value its importance. But some problems don't respond well to these techniques. As well as learning how to attack the problem directly, we need to be able to tackle it indirectly.
Here are three other approaches which may be useful.
Very few problems are completely new to us. We have generally encountered similar problems in the past, or heard about similar problems other people have encountered.
We have also probably encountered other problems with the same object, or in the same area: this computer is always going wrong, or that member of staff is always causing difficulties.
Our previous experience tends to direct our attention to one specific aspect of the problem.
Our previous experience may help us to focus on the key elements of the problem - or it it may, on this occasion, be completely misleading.
If a problem is not responding, try listing all the aspects. Brainstorm everything which may be a factor. If someone with no previous experience was presented with this problem, what would they ask about?
If a computer is going wrong, is it the software? The hardware? The power supply? The network connection? The user? Or some combination of the above?
Every problem has a frame. As soon as you think about a problem, you place it in some context.
The frame may be the wrong size, or in the wrong location.
If you change the frame, the facts of the problem may not change, but your feelings probably will: how you feel is largely determined by the frame around the problem. When you are watching a film and see someone falling over or being dumped by their girlfriend, it can be comedy or tragedy, depending on how you see the rest of the film.
The frame also determines the scope of the problem, and hence the range of resources available to tackle it.
Changing the frame may change the nature of the problem. What is seen as a problem may also be seen as perfectly normal and healthy behaviour from another perspective. "My teenage child is keeping secrets from me." But it is healthy for a teenager to hold back some information from their parents - it is part of the process of growing up. So how do you establish what is right and appropriate for them to tell you (and why?!) and what they can reasonably keep secret?
Western societies are more individualistic today than in the past. We often see problems as affecting the individual, so we look for solutions which apply to the individual. But what changes if we see the individual as part of a group - a family, a community, a team?
Go back and check the foundations of the problem.
What are my assumptions? For each assumption, I may be able to change the focus, frame or foundation.
Is this a problem which actually needs to be fixed? By me? Now?
What is the likely consequence of not fixing the problem?
What is the likely consequencce of partly fixing the problem? Or changing it?
Will fixing the problem create other problems - possibly more difficult ones?
If the problem is fixed, what else is likely to change?