Prove that either
a) this problem is solvable
or
b) this problem is unsolvable
Let assume that (a) is true then the solution to this problem is that it is solvable which points to (a) and this is an easy assumption. Now lets assume that (b) is true then we might say that that the solution to this problem is that it is unsolvable but by the fact that we admit that the problem unsolvable we actually solved the problem. And by solving the problem we point again to (a).
Therefore I believe that the problem is solvable.