MATH.23:2 - Problem

A list of successful cases leaves many possible general claims. A formula can match every computed value and fail beyond them. A proposed proof can depend on a property absent from the conjecture. Conversely, a failed conjecture can reveal a useful operation or a stronger question.

The difficulty is to extract a relation that can be investigated generally. Changing a number produces another instance; changing the construction law, allowed maps or quantifier can create a new problem. The latter change needs a mathematical reason and a feasible first attack.