A Magic Trick?

A magician and her assistant perform the following trick with a chess board and 64 pennies.

The assistant first blindfolds the magician, and then calls for a volunteer from the audience. He asks the volunteer to point at one square on the chessboard. He notes the square that was selected, then gives the volunteer the 64 pennies, and asks him to place one penny on each square of the chessboard, each penny randomly showing heads or tails.

The assistant then flips exactly one penny, and removes the magician's blindfold. The magician then studies the board, and announces the square that the volunteer picked.

For this problem, of course, the magician uses no information other than the pattern of the pennies on the chessboard. How is the trick performed?

Solution