Hex could be the perfect abstract board game. It has the simplest rules of almost any known game, yet is remarkably difficult to play well.


Two players, Black and White, own opposite edges of the board. The board is initially empty.

  • Players take turns placing a piece of their colour in an unoccupied hexagon.
  • The game is won when one player establishes an unbroken chain of their pieces connecting their sides of the board.


The following additional rule is recommended to address the opening player's huge (winning) first move advantage:

  • The player to move second has the choice of swapping colours, effectively stealing the first player's move.

A game won by White.

This simple rule set gives Hex excellent clarity, which means that players are not distracted by peripheral rules or ambiguous goals and may concentrate fully on strategic analysis. The swap rule mentioned above does not compromise the game's clarity and in fact adds a dimension of strategy.

The small 3x3 game on the right shows a simple introductory puzzle suggested by Tim Robinson: Prove that B2 is an easy win for the opening player.

What other opening moves are also a guaranteed win for the first player on the 3x3 board?

This demonstrates the potential strength of the opening move and the need for the swap rule.

Here is a page of blank 11x11 boards to practice on. Board sizes are commonly 10x10 or 11x11 but can be any size within reason. Contact me if you'd like blank EPS diagrams of other board sizes or solutions to puzzles.

White to play and win (Piet Hein).

Hex was invented independently by mathematicians Piet Hein and Nobel laureate John Nash in the 1940s. Disappointingly Hex did not feature in the recent dramatised film version of Nash's biography A Beautiful Mind, despite them managing to slip in a couple of games of Go.

The simple puzzle on the left was created by Piet Hein over 50 years ago.

Hex has some interesting mathematical properties including:

  • It's not possible for a game to end in a tie - one player must win.
  • It's been proven that the opening player has a winning line, but no one has yet discovered exactly what that winning line is.


Hex features in a number of mathematics texts and research papers, though surprisingly there had been no books specifically about the game throughout its 50 year history. I took advantage of this fact to write Hex Strategy: Making the Right Connections in 2000. It has received good reviews from popular journals and magazines including Scientific American and the Journal of Recreational Mathematics, in addition to more specialised publications such as Abstract Games Magazine.



Just before Hex Strategy went to press, news emerged that Jack van Rijswijck was also in the process of preparing a book on the game. Jack has been studying Hex for years with the University of Alberta GAMES Group, and in conjunction with graph theorist Ryan Hayward would no doubt have revealed some fascinating insights into the game from a position of mathematical authority. This would have nicely complemented the approach taken in Hex Strategy, which is more a look at Hex from a player's perspective with only moderate investigation into the underlying maths. Unfortunately it sounds like both projects covered too much common ground and Jack and Ryan have put their book on hold, a great pity.


I've also published a series of articles on Hex in Abstract Games Magazine (here's the introductory article). This series started out summarising the key elements covered in the book, but has since become an outlet for puzzles and new ideas about the game as they develop.

Article #4 in the series described a simple algorithm that plays a surprisingly strong game given its lack of strategic knowledge and search. You can download the Hex Maniac executable for Windows here and the C++ source code for a simplified command line version here. Bear in mind that Hex Maniac is really just a proof-of-concept and not a strong opponent. For a good computer player for PC you need look no further than Vadim Anshelevich's Hexy, or there is a Mac player called Hexomania. A Zillions of Games rules file for playing Hex can be downloaded here.

Black to play and win (John Tromp). My favourite puzzle - it's hard!

Visit Jack's page of Hex links and the dmoz Open Directory Project Hex page for good lists of online Hex resources.

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Site designed by Cameron Browne © 2002. Last modified 18/7/2007.