Maybe you are aiming at a different audience, but this conundrum is similar to how most research problems in pure sciences go -- problem might seem interesting,

Maybe you are aiming at a different audience, but this conundrum is similar to how most research problems in pure sciences go -- problem might seem interesting, but finding the solution is hard and sometimes we don't even know if a solution exists. Mathematicians often use the words "existence" and "uniqueness": Does a solution to the problem exist and if it does, is it unique? George Polya's How to Solve It consists of essays on how to approach problems in general (not necessarily exclusive to mathematics in my opinion). You can find an excellent summary at https://math.berkeley.edu/~gmelvin/polya.pdf https://math.berkeley.edu/~gmelvin/polya.pdf. Essentially, the advice boils down to: 1. use the defining features of the set up 2. give things/variables meaningful names 3. leverage symmetry 4. try describing one object in two different ways 5. draw a picture, flowchart to visually represent 6. ask a simpler version of the problem by removing some constraints or considering very specific cases 7. read a lot and think about problems a lot