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John Nash proved in 1952 that a game of cette application cannot end in a tie, and that for a symmetric board there exists a winning strategy for the player who makes the first move (by the strategy-stealing argument).  cette application is a strategy board game played on a hexagonal grid, theoretically of any size and several possible shapes, but traditionally as an 11×11 rhombus.  The turn of each player is shown by a red or blue disc on a side of the board game.  cette application is an abstract strategy game that belongs to the general category of "connection" games.  According to the book A Beautiful Mind, John Nash (one of the game's inventors) advocated 14×14 as the optimal size.  The goal is to form a connected path of your stones linking the opposing sides of the board marked by your color, before your opponent connects his or her sides in a similar fashion.  The first player to complete his or her connection wins the game.  The game was invented by the Danish mathematician Piet Hein, who introduced it in 1942 at the Niels Bohr Institute.  Players take turns placing a stone of their color on a single cell within the overall playing board.  Other popular dimensions are 13×13 and 19×19 as a result of the game's relationship to the older game of Go.  Each player has an allocated color, Red and Blue being conventional.  The player must touch a cell to fill it with his own color.  When the move is done, the turn comes of the opponent player.  It was independently re-invented in 1947 by the mathematician John Nash at Princeton University.  However, the argument is non-constructive: it only shows the existence of a winning strategy, without describing it explicitly.  After that, he can cancel his last move using the 'Undo' button, and redo a different move.  Finding an explicit strategy has been the main subject of research since then.  The four corner hexagons each belong to both adjacent sides.