If you can actually prove that your problem is unsolvable, you’re pretty much stuck.

For example, you could show how your problem is a variation of an existing unsolved problem.

More frequently though…

On your path to showing how your problem cannot be solved, you’ll get stuck. Something about your problem isn’t actually unsolvable, or something about your problem doesn’t match any of the unsolved problems.

It’s this sticky point where you have a new problem to solve.

For this new problem, apply the problem-solving checklist for more ideas about solving problems.