The problem above is indicative of a problem that often occurs in mathematics. This particular one comes up in the Abstract Algebra course I teach.
We first determine if there are any solutions (and could there be more than one) and THEN we look to find those solutions. The strategy on approaching the problem is certainly different if you must verify there is no solution, find the ONLY solution, or find all the solutions.
Most religions pose some sort of a solution to the sin problem. Perhaps they provide many proposed solutions. Perhaps the claim is there is no solution. Perhaps they pose the idea there is a solution, but don’t actually provide it.
Jesus claims He is the only solution: John 14:6 “I am the way, the truth, and the life. No one can come to the Father except through me.”