The difficult thing is to divide a big problem into a set of smaller ones that together solve the problem BUT such that those smaller solutions are valuable on

The difficult thing is to divide a big problem into a set of smaller ones that together solve the problem BUT such that those smaller solutions are valuable on their own, not only as part of the bigger solution that is your eventual goal. So the problem is not so much to solve a problem but to FIND a problem whose solution is useful on its own and perhaps also as a sub-solution to bigger problems.