If you find this puzzle too hard or too easy, you can press +/- to add or remove buttons. Also, see the paper referenced below for a short proof that the player can always win this game (by induction on the number of buttons).
For proof of existence of a winning strategy, optimal strategies for the player and for the machine, and how this game emerged from a control theoretic problem, see:
A Combinatorial Game Approach to State Nullification by Hybrid Feedback In the proceedings of the 46th IEEE Conference on Decision and Control, CDC 2007.
