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RE: Does intuition matter in solving problems?
Sometimes, when I've got problem solving to do, instead of focusing on the problem at hand, I make sure I've absorbed all the information regarding it, then just 'sit on it' push it out of my conscious mind for some other part of me to work on. Then, after a while DING, the metaphorical light bulb goes on. Would that be called intuition?
I think there may be some more formal definition of intuition but I'm not the expert in philosophy / psychology so I dare not to give a rigorous definition. In my own words, intuition is a process of thinking unconsciously and arriving at the conclusion without step-by-step analytics. It seems like you undergo some sort of thinking on the problem and get the solution after the "ding". In my opinion, intuition is more like getting the solution which we don't know how and which may not be but most of the time is correct. So it seems like your case is a little bit not the same as intuition. I can't really formalize my thoughts and so sorry for not being able to write in simple words : )
The book "Pragmatic Thinking and Learning" describes this process and really got my problem-solving skills to a whole new level. I think it will also provide a lot of background for better understanding intuition, @manfredcml