Marco and Leonardo decided to play a game on a checkerbard of 4×4 squares. The board is initially filled with two-sided identical coins.
The game notes that these two players play turns alternatively where the both players are permitted to flip the coins on any 2×2 size square or a line of 1×4 fom side A to side B .
The first person who finishes the game with all 4×4 board pieces turned to the B side wins.
Prove that player 2 is always bound to win
After some members' interventions i imposed some rules and reduced the board size to make the problem within any one's grasp .
any player cannot repeat his last or his opponent's last move
and moreover , any player is always prioritized to take action of biggest number still available of A sided coins ( for example a set containing 3 non flipped coins is a priori to be played than any set having 2 or 1 non flipped coins)