Puzzle: Magic Square
October 29, 2013 § 7 Comments
Hello Math people. I heard this puzzle a few weeks ago, and I thought it was pretty great. Here is how it goes:
You and a friend are playing a game against an adversary. The game is played as follows. You walk into a room with the adversary, leaving your friend outside. The room contains a checker board (the typical 8 by 8 kind), and each square has on it exactly one coin. Each coin can either be heads-up or tails-up. Then, the adversary chooses exactly one square which he calls the magic square. You, then, based on the arrangement of the coins and which square is the magic square, will choose exactly one square and turn its coin over (either from heads-up to tails-up or from tails-up to heads-up). Then, you will leave the room through a back door and wait in a separate room. Your partner then comes into the adversary’s room, looks at the board, and proceeds to take a guess at which square is the magic square. If your partner guesses correctly, you win.
Assuming you and your partner have no idea of what arrangement the board will be in when you enter the room, come up with a strategy for you and your partner to use so that you can always win.
Note: the only information you or your partner can have from looking at a coin is which square it is on and whether or not it is heads-up. The solution does not involve doing something silly by rotating the coins; the adversary chooses the orientation of the coin after you flip it.
Thanks for reading, and feel free to message me if you would like the answer!
-A Student of Logic