Friday Puzzler -- Othello Pieces
Alex Y
For those not familiar with Othello (the game), the pieces are checkers-like disks, white on one side and black on the other. The puzzle below could just as easily be done with coins, and with boxes containing and hiding the objects rather than a blindfold.
You sit in a chair in front of a lazy susan that has four Othello pieces arranged in a square. One is black side up, and the other three are white. You are then blindfolded and told that you need to get all the pieces to be the same color in a few turns as possible.
A turn in this game consists of my rotating the lazy susan so that you can't tell its orientation versus the previous turn. You can then choose how many of the disks to flip, and which ones to flip. Flipped disks must be put back in the same spot. There is no way for you to tell which pieces have been flipped in previous turns.
After each turn is complete, I tell you whether or not you have gotten them all the same color (i.e., if you choose to flip two disks, and the first one you flip makes them all the same color, that is NOT a solution).
What is the minimum number of turns with which you can be 100% certain of winning this game. What is your strategy?