Hex is a two-player game invented by Piet Hein in 1942 while a student at Niels Bohr's Institute for Theoretical Physics, and subsequently and independently by John Nash in 1948 while a mathematics graduate student at Princeton. The game was originally called Nash or John, with the latter name at the same time crediting its inventor and referring to the fact that it was frequently played on the tiled floors of bathrooms (Gardner 1959, pp. 74-75). The name Hex was invented in 1952, when a commercial version was issued by the game company Parker Brothers. Hex is played on a diamond-shaped board made up of hexagons. The game is usually played on a boards of size 11 on a side, for a total of 121 hexagons, as illustrated above. In the game, one player plays white pieces, while the other plays black, with play alternating between players and placement only allowed on unoccupied hexagons. Alternate sides of the board are designated white and black as shown above, and the goal of the game is to complete a chain of pieces between one player's two sides. The game cannot end in a draw since no chain can be completely blocked except by a complete chain of the opposite color.