Unfortunately, most problems aren't. You need a problem where you both know what the solution looks like or can otherwise very quickly and efficiently determin

Unfortunately, most problems aren't. You need a problem where you both know what the solution looks like or can otherwise very quickly and efficiently determine that a solution is correct, but at the same time can't work out a correct solution with a similar amount of effort/time/cost as it took to determine how to verify a solution. Most problems don't match that criteria. You usually either have a problem with a known method of solving, or you have a problem with no clear way of verifying the solution besides the act of finding the solution itself which would involve in some way proving it is correct, or you have a problem where verifying a solution takes a very long time or has a high cost or even can't be done more than once, so you need to try to determine the best solution without being able to actually test or verify. Basically all problems just don't fit the "hard to solve but easy to verify" criteria to a degree that makes llms a good fit. On the other hand, there are so many problems that even a tiny fraction is a relatively large number.