- Mathematics/physics textbook problem: can you prove it has no solution? E.g. you can start by assuming it has and then find a contradiction. That also works for finding a solution.
- Programming: can it be done by a series of pen-and-paper operations? If yes, then it has solution and you must keep on trying. Can you find an equivalence between your problem and and a well known problem? This last point is true also for math/physics.
On equating your problem with a well-known one: there are not so many new things under the sun. Try to formalize the problem statement, then you might come to conclusions of the form:
- This is equivalent to solving the traveling salesman (bad for you)
- This is essentially a system of linear equations (good)
When you do this you can take advantage of all existing literature, i.e. the knowledge of smarter people.
- Mathematics/physics textbook problem: can you prove it has no solution? E.g. you can start by assuming it has and then find a contradiction. That also works for finding a solution.
- Programming: can it be done by a series of pen-and-paper operations? If yes, then it has solution and you must keep on trying. Can you find an equivalence between your problem and and a well known problem? This last point is true also for math/physics.
On equating your problem with a well-known one: there are not so many new things under the sun. Try to formalize the problem statement, then you might come to conclusions of the form:
- This is equivalent to solving the traveling salesman (bad for you) - This is essentially a system of linear equations (good)
When you do this you can take advantage of all existing literature, i.e. the knowledge of smarter people.