You and your friend find yourselves in a room with the Devil. The Devil tells you that he wants to play a game. If you win, the Devil will let you go. If you lose, the Devil takes your souls.
Here are the rules of the game:
You and the Devil will be in a room with a chessboard with coins on it, one on each square. Meanwhile, your friend will be outside the room. The coins will be randomly distributed heads and tails. The Devil randomly chooses one of the squares and calls it "the magic square". Next, you may flip one coin on a square. Then your friend will come in, and must tell which "the magic square" is by merely looking at the board.
Details:
-
You may flip a coin. You may choose not to flip a coin.
-
You and your friend will agree upon a strategy, before the game starts, so you are both aware of the strategy.
-
Your friend will not see the chessboard when the coins are initially put on the board, i.e. cannot see a before-and-after difference after you potentially flipped a coin.
-
You cannot use any other means to communicate with your friend during the game, other than the coin flip.
What will your strategy be?