the game is not unwinnable for every choice of a,b,c since one scenario is the following:

a = 1, b = 2, c = 3.

move 1: move 2 marbles from pile c to pile b. now pile 1 has 1, pile 2 has 4, and pile 3 has 1, game over.

this suggests that you try to show the game is winnable.