This is the kind of post that I'll read tomorrow and wonder what on earth I was on about.
Anyway, I wonder if anyone else shares my problem solving method. When solving difficult problems it's easy to get bogged down with thoughts of "I can't do this" or "It's not possible". Well to that I say piffle and boulderdash!
Why not approach the problem from the opposite way round? Mentally jump to a future time when the problem (or puzzle) is solved. Now you know it has been solved so you know it's possible. From this you can almost see the solution. Thoughts that come to my head are "ok it's possible, so I guess I must have......". Perhaps I have explained it badly but hope at least one person gets where I am coming from.
I guess this post was influenced by the More then meets the eye post. If we 'know' the puzzle exists already (in a future time) then it's easier to find it.

I get what you mean, and have done this myself. I'll imagine the finished result and then figure out how to get (the problem) to be like that. Problem solved

Interesting idea. I've always said that sometimes the best way to solve a maze is to work backwards. This is especially true when solving puzzles. I know that the solution exists, as I've seen it in front of me before I scrambled it!

I think that although this speaks to having the commitment in seeing a task through, as well as finding the faith that the solution does exist, I think the essence of problem solving has more to do with a pragmatic "trial and error" process born out of repeated attempts. The process of puzzling over a problem, trying all avenues leading to dead ends, feeling that there is no hope, leaving the problem,, returning with a new perspective, having a moment of inspiration, which may or may not lead to an answer, until eventually the task is seen through is really at the heart of successful problem solving. All the while, with each puzzle or problem solved, new insights into some underlying principal can be ascertained which will make success with the next dilemma all the quicker and more assured.
When it comes to designing, that's a whole different story if you've never actually seen the finished product.

Have you ever set out to design/build a puzzle only to find that the finished product is much different then you thought, but still quite remarkable in its own right? Can you think of any examples of that?

Have you ever had to concede the inability to create what you imagined, leave it half done on your shelf, coming back sometimes years later to complete it? Any examples of puzzles like that?

Along the same lines, I think competition really fosters innovation in solving for fewest moves. There are a number of puzzles that have seen huge improvements due to people saying "how the heck did so-and-so get XYZ moves??" and then coming up with an even better method.

When you don't know what is possible you'll often settle for a good solution instead of assuming that there is an amazing solution waiting to be found. Only when somebody beats your score to you go back an revisit your strategy to try to beat them.

Solving evolution at work .

Looking back at my post I realised I left out an important part. It sounds like I am only talking about puzzle solving or maths problem. However I meant it in much broader terms. In my case I will use it for making puzzles and also in life's little problems that arise. Those situations where you can't see a way out or decide what to do. Jumping ahead and kind of predicting what you did helps you decide. I can imagine it being useful if you get into the situation where you suddenly cannot pay the bills. I guess it's just a form of positive thinking and focussing on what you can do instead of what you can't.

I recently read an article in a psychology magazine about this. They asked people to solve certain problems. Half of them were asked to think about other things before hand, the other half were asked to visualize the end result as if they had already solved the problem. The latter did worse, actually.
When we convince ourselves we've already solved the problem before even attempting it, our brains just aren't as focused on the task.

However, I don't know how this applies to solving puzzles.

Excellent point, and I'm glad you bought that research up. You beat me to it! The scenario is the same as the kid who focuses completely and thoroughly on getting a present, and can think of nothing else. Upon buying him the present, after a day of using it, the kid almost completely loses interest and ceases to think about it much at all. This isn't because the toy is less interesting then he thought, but because the knowledge of having it took away his focus on it.

A problem arises when a person has a goal but does not know how this goal is to be reached. Whenever one cannot go from the given situation to the desired situation simply by action, then there has to be recourse to thinking.

In studies, people who were mostly students of universities or of colleges, were given various thinking problems, with the request that they think aloud. The subject who is thinking aloud remains immediately directed to the problem, so to speak allowing his activity to become verbal. This is a technique I frequently use to problem solve. It's a form of "instructing" myself, but also challenging my thinking and being my own "devil's advocate.

What has also been born out by research is that the classic thinking of solving puzzles increasing your cognitive abilities and staving off dementia has also been shown to not be quite right. They found that what did was, in effect "train" the subjects on how to solve that "particular" puzzle faster and more effectively, but did little for overall cognitive development, which is a global brain process that can assist in broad problem solving. Interestingly, what the research did find is the single best thing that was shown to help with this was taking long walks or runs. This makes sense, as when we do this, our brains are immediately engaged in all our senses as we analyze our environment, seek out the interrelationship of what's around us, remember where we are, and plan where we're going. Having evolved from a largely nomadic people, this makes evolutionary sense.

In short, if you run into problems with your task, be in puzzle building or puzzle solving, or even other dilemma's with work, family or finance, then put the puzzle on the shelf, go outside, and go for a run/walk for at least 30 to 45 minutes. You will potentially find moments of inspiration to see you through or, at least, reset your mind so that you can redirect yourself to the task.

This issue is of great interest in artificial intelligence (AI), as if we can learn the techniques the brain goes through to problem solve, then we can design machines that can do that to! It is obvious that the memorization of a great number of facts will not take you all the way.

Here are some techniques that can help:
Abstraction: solving the problem in a model of the system before applying it to the real system (ok, so if I ignore the shapeshifting of this mod and solve it just like a cube, then it will work!)

Analogy: using a solution that solved an analogous problem (ok, so this corner turning octahedron looks just like a 3x3 mod, so I'll use the same algorithms as a 3x3 to solve it!)

Brainstorming: Suggesting a large number of solutions or ideas and combining and developing them until an optimum is found (ok, so if I want a Transformer cube, I'll just post the problem on tp forum and and see what they come up with! Hint hint!)

Divide and conquer: breaking down a large, complex problem into smaller, solvable problems (I'll just reduce my 4x4 to a 3x3 and then solve it as such!)

Hypothesis testing: assuming a possible explanation to the problem and trying to prove (or, in some contexts, disprove) the assumption.

This last one is in essence what Tony was talking about, which is a viable problem solving technique.

Sorry for the long winded response, but this is a field I'm very excited about!

The problem with those kind of research results is that the people were obviously given tasks to solve. I am talking about ones that we desire or really need to solve. It has to mean something to us.