Hex was invented by mathematician and poet Piet Hein in 1942 and independently by John Nash in 1948. It is traditionally played on an 11×11 rhombus board, although 13×13 and 19×19 boards are also popular.
Hex is a special case of the "node" version of the Shannon switching game. As a product, Hex is a board game; it may also be played with paper and pencil. ==History== ===Invention=== The game was invented by the Danish mathematician Piet Hein, who introduced it in 1942 at the Niels Bohr Institute.
Although Hein later renamed it to Con-tac-tix, it became known in Denmark under the name Polygon due to an article by Hein in the 26 December 1942 edition of the Danish newspaper Politiken, the first published description of the game, in which he used that name.
Hex was invented by mathematician and poet Piet Hein in 1942 and independently by John Nash in 1948. It is traditionally played on an 11×11 rhombus board, although 13×13 and 19×19 boards are also popular.
The game was independently re-invented in 1948 by the mathematician John Nash at Princeton University.
Hex is currently published by Nestorgames in a 11x11 size and a 14x14 size. ===Shannon's Hex machine=== About 1950, American mathematician and electrical engineer Claude Shannon and E.
The game was first marketed as a board game in Denmark under the name Con-tac-tix, and Parker Brothers marketed a version of it in 1952 called Hex; they are no longer in production.
Gardner was unable to independently verify or refute Nash's claim. ===Published games=== In 1952, Parker Brothers marketed a version.
The first exposition of it appears in an in-house technical report in 1952, in which he states that "connection and blocking the opponent are equivalent acts." The first rigorous proof was published by John R.
According to Martin Gardner, who featured Hex in his July 1957 Mathematical Games column, Nash's fellow players called the game either Nash or John, with the latter name referring to the fact that the game could be played on hexagonal bathroom tiles.
Hein wrote to Gardner in 1957 expressing doubt that Nash discovered Hex independently, but Nash insists that he reinvented the game before being exposed to Hein's work.
Pierce in his 1961 book Symbols, Signals, and Noise.
Parker Brothers also sold a version under the "Con-tac-tix" name in 1968.
Hex was also issued as one of the games in the 1974 3M Paper Games Series; the game contained a 50-sheet pad of ruled Hex grids.
In 1979, David Gale published a proof which also showed that it can be used to prove the two-dimensional Brouwer fixed-point theorem, and that the determinacy of higher-dimensional variants proves the fixed-point theorem in general.
Various paradigms resulting from research into the game have been used to create digital computer Hex playing automatons starting about 2000.
They extended the method to weakly solve the center pair of topologically congruent openings on 8×8 boards in 2002 and the center opening on 9×9 boards in 2003.
They extended the method to weakly solve the center pair of topologically congruent openings on 8×8 boards in 2002 and the center opening on 9×9 boards in 2003.
Starting about 2006, Monte Carlo tree search methods borrowed from successful computer implementations of Go were introduced and soon dominated the field.
In 2009, Philip Henderson, Broderick Arneson and Ryan B.
In 2013, Jakub Pawlewicz and Ryan B.
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