The Berlekamp switching game is a mathematical game proposed by American mathematician Elwyn Berlekamp. It has also been called the Gale–Berlekamp switching game, after David Gale, who discovered the same game independently, or the unbalancing lights game. It involves a system of lightbulbs controlled by two banks of switches, with one game player trying to turn many lightbulbs on and the other trying to keep as many as possible off. It can be used to demonstrate the concept of covering radius in coding theory. Rules The equipment for playing the game consists of a room containing rectangular array of lightbulbs, of dimensions for some numbers and . A bank of switches on one side of the room controls each lightbulb individually. Flipping one of these switches changes its lightbulb from off to on or from on to off, depending on its previous state. On the other side of the room is another bank of switches, one for each row or column of lightbulbs. Whenever any of these switches is flipped, every lightbulb in the row or column that it controls changes from off to on or from on to off, depending on its previous state. When flipping more than one switch, the order in which the switches are flipped does not make a difference to the outcome: the same lightbulbs will be lit at the end of the sequence of flips no matter what order they are flipped. The game is played in two rounds. In the first round, the first player uses the switches that control individual lights, to set the lights on or off arbitrarily. In the second round, the second player uses the switches that control rows or columns of lights, changing the pattern of lights set by the first player into another pattern (or, possibly, leaving it unchanged). The goal of the first player is to have as many lights remaining lit at the end of the game as possible, and the goal of the second player is to have as few lights remaining lit as possible. Therefore, the first player should choose a pattern of lights for which the second player cannot turn off many lights. History Berlekamp worked at Bell Labs in Murray Hill, New Jersey from 1966 to 1971. While there, he constructed a physical instance of this game for the case in the Mathematics Department commons room. David Gale also invented the