The Game of Hex
Abstract
Hex is a two person game played on an
n x
n
board in which the players take turns trying to construct paths
from one side of the board to the other. It is known that there exists a
winning strategy for the first player, but no one has yet been able to find such a strategy
for any board larger than
9 x
9.
Despite this, one can ask the following two questions: "what is
the shortest path with which player one can guarantee a win?" and "what is the minimal
number of moves play one must make to guarantee a win?" These are questions
of
optimal play in the game and the primary goal of these
pages is to give lower bounds on answers to these questions
and provide a number of conjectures and "challenges."
Table of Contents
Complete List of References
- [AS1]
Abstract Strategy.com,
http://www.abstractstrategy.com/hex.html.
- [GD1]
David Gale,
The game of Hex and the Brouwer fixed point theorem.
American Mathematical Monthly,
86(10): 818 — 827, 1979.
- [GM1]
Martin Gardner,
http://en.wikipedia.org/wiki/Martin_Gardner.
- [GM2]
Martin Gardner,
Mathematical Games: Concerning the game of Hex, which may be played on
the tiles of the bathroom floor.,
Scientific American, page 144ff, July, 1957.
- [GM3]
Martin Gardner,
The Scientific American Book of Mathematical Puzzles and Diversions,
volume 1, chapter: The Game of Hex, pages 73 — 83.
Simon and Schuster, New York, NY, 1959.
- [HP1]
Piet Hein,
http://www.piethein.com/usr/piethein/HomepagUK.nsf.
- [HW1]
The Hex Wiki,
http://www.hexwiki.org/.
- [NJ1]
John Nash,
http://nobelprize.org/economics/laureates/1994/nash-autobio.html.
- [PC1]
Carl Pomerance,
personal communication.
- [SI1]
Ian Stewart,
Hex marks the spot.
Scientific American, pages 100 — 103, September, 2000.
- [VJ1]
Jack van Rijswijck,
Hex opening theory.
- [YJ1]
Jin Yang, Simon Liao and Mirek Pawlak.
A decomposition method for finding solution in game Hex 7x7. In
International Conference on Application and Development of Computer
Games in the 21st Century, pages 96 — 111, November, 2001.
- [YJ2]
Jin Yang, Simon Liao and Mirek Pawlak.
Another solution for Hex 7x7.
Technical Reoprt, University of Manitoba, 2002.
- [YJ3]
Jin Yang.
Jing Yang's Homepage.
