After the incidents of Skyfall, 007 remembered a quote Q had said when he was accessing Silva's Omega site :
It's like solving a Rubiks cube that's fighting back.
007, intrigued by this statement, asks the following:
Starting from a completely shuffled Rubik's cube, for every 18 moves you make, the Rubik's cube makes 2 moves. The Rubik's cube is defeated if you can solve it. The Rubik's cube cannot reverse any moves you made in your last attempt, and the same holds for you. But the reverse moves can be used if the cube is at a different state than when the attempt started. Given that the cube plays optimally, can the Rubik's Cube be defeated?
Q thinks for a bit and says, possibly not. But he doesn't know. It's up to us to prove him right or wrong.
But Q does asks the following:
Generalizing this, if you can make $n<20$ moves, and the cube can make $m\le n$ moves, then for what $n$ and $m$ is the cube defeatable, if at all?
A related problem can be found here