You have a standard checkerboard with 64 squares and a coin in each square, randomly facing heads or tails up. There is an evil monster in the room with you and he arbitrarily selects some square and tells you that it is the magic square.
You are allowed to flip one and only one coin on any one square of your choice. Then your friend comes in and he is supposed to guess the location of the magic square correctly, without any help from you. You and your friend are allowed to discuss some strategy beforehand..
What strategy should you use so that you and your friend won't be eaten by the monster? (a.k.a your friend is able to choose the correct square?)
The question has a mathematical/logical answer, and it is all pure strategy. So no answers that try to go around that please :)