When solving problems after you have exhausted the normal means of coming up with the solution, think in terms of unorthodox methods. Vary your thinking and try to solve the problems by creating something completely new and irrelevant. Come into the problem through the "back door".
Research and curiosity go hand in hand in solving the toughest problems. Quite often the answer is so simple, it is not obvious to us. Use an organized plan to work with and record the results logically so you will have a format to follow and a basis for review as you proceed to create something new or solve an "unsolvable" problem.
Creating new programs or products by association is another method of thinking. You first think of an object which is similar or adjacent to the subject item, then continue the "chain" of associated thoughts until new and useful programs or products emerge as ideas. Relate these ideas to the subject item by trial and error or by analysis of all the variables involved.
Plain old fashioned "daydreaming" is another method of creative thinking. Make up a fantastic story in your mind and try to visualize (dream) your way to a successful conclusion based on what results you are trying to achieve.
Consider all the alternatives to what you're trying to come up with. Gather together and analyze all the data you can find about the subject. If you get into a rut, leave it lie. Go to some other aspect of the puzzle. come back to it later. Quite often as you progress it will suddenly appear, bright and clear. When it does, write it all down so you won't lose it as your mind drifts to the next step.
Complete one step at a time. By breaking it down to size you can solve it in segments. Don't try to override your mistakes.
Recognize them and bury them so they will help, not hinder, your progress toward your creative goal.
Don't further confuse the issue by doing so much study and research that there are too many roads to take.