Certain mental states induced by meditation are common with those states specific to mental processes that get your undivided attention like studying something you find interesting or that involves creativity. Your mind is naturally focused but relaxed in those states.

You are so focused that even the perception of the passing time becomes irrelevant. You do not hear the noise around you. Your limbs get numb after so long, motionless period of time when you "forgot" you had them. Did it happen to you?

Creativity flourish in these moments. It is like "divine inspiration" is bestowed upon you. Supposedly artistic masterpieces were created in such a state. Similar with significant scientific discoveries (I always wondered where did Einstein got this idea of relativity when nothing in day by day life was hinting toward it).

And this is how you can enhance your problem solving capacity. Because ideas and solutions are all about creativity. So, just allow your mind focus on the problem by discarding the associated emotions. That is when meditation helps a lot.

So how you do find solutions to your problem? Very simple:
Write down the problem and the hopes and fears associated with that problem. In five to ten minutes exhaust everything that you think about it. This has multiple benefits. First of all it crystallizes the problem with the pros and cons and allows you see how important the resolve of this problem is for you. It makes it more finite, if you wish. Emotions tend to make a problem bigger that it is, you know. Secondly, it allows you look, literally, at that problem from outside rather than identifying yourself with it. And this will make you objective when solving the problem. Now, just clear your mind of the problem by closing your eyes and spend another five to ten minutes in meditation. Still your mind and try to keep it focused on a mantra, your breath or other object of your choice for as long as you can. This is not simple task. You will find yourself thinking to something else, or eventually to your problem. Just gently, bring your attention back to the object of meditation. Through meditation your mind breaks free from the addictive habits of hope and fear. Meditation also calms, relaxes and refresh the mind and it prepares it to … find a solution.

So at the end of that period, you realize that there has been a shift in your perspective and there is an answer to the problem, or just as often, you will go about your day and the answer or the perspective shift will come later with the best resolve for you. That is because you removed the emotional cluster and the confusion usually associated with problems you perceive as unsolvable.

"Sleep over it" is the same thing. With meditation though you do not have to take a nap each instance you need to solve a problem.

Constantine George
Do you know how to meditate? If not, follow the link: How to meditate. For similar techniques that improve your mind and make you feel happy, check: Better mind.
http://www.better-mind.com/