IT-CESENATICO 2013 Problem 6

Two magicians are performing the following game. Initially the first magician encloses the second magician in a cabin where he can neither see nor hear anything. To start the game, the first magician invites Daniel, from the audience, to put on each square of a chessboard $n \times n$ , at his (Daniel's) discretion, a token black or white. Then the first magician asks Daniel to show him a square $C$ of his own choice. At this point, the first magician chooses a square $D$ (not necessarily different from $C$ ) and replaces the token that is on $D$ with other color token (white with black or black with white). Then he opens the cabin in which the second magician was held. Looking at the chessboard, the second magician guesses what is the square $C$ . For what value of $n$ , the two magicians have a strategy such that the second magician makes a successful guess.