Friday Afternoon Lifesavers – the Teacher’s Best Friend; Part 6, The Game of Hex

Friday Afternoon Lifesavers are exactly what they sound like: at the end of the week when you and your students are running out of gas, these activities come to the rescue. They are mathematical, engaging, fun, and give the teacher a much-needed break.

INTRODUCTION: Hex is a board game played on a grid made of hexagons. It can be played on a board of different sizes; the graphic above shows a typical 11×11 game board in the shape of a rhombus.

HISTORY: The game was invented by the Danish mathematician Piet Hein, who introduced the game in 1942 at the Niels Bohr Institute. It was also independently invented by the mathematician John Nash in 1947 at Princeton University. In 1952 Parker Brothers marketed a version and called their game Hex, as it is known today.

GAME PLAY: Players take turns claiming a hexagon of their color. The goal is to form a connected path of your color linking the opposing sides of the board marked by your colors, before your opponent connects his sides in a similar fashion. The first player to complete his connection wins the game. The four corner hexagons each belong to both players. John Nash proved that the game can never end in a tie. The only way to prevent your opponent from forming a connecting path is to form a path yourself, thereby winning. (N.B. – information edited from wikipedia.org)

From Mr. L – Here’s a downloadable pdf. file with five different size game boards. I’d suggest that beginners start with the 7×7 game board, then work their way up to the 11×11 board as they gain skill and familiarity with the rules and strategy. It’s also a good idea for the teacher to model this on the overhead projector or LCD projector before students play. This is a game of strategy, and there is a lot of learning going on, even though we “can’t see it.” The 1973 movie Paper Chase, starring John Houseman playing a Harvard law professor, has a great line, which I’ll paraphrase. John Houseman is talking to his students, saying: “You will learn the law, but I will train your mind.” This is how I feel in the classroom working with students and also in training seminars working with teachers. Mathematics can be found in books, but how to think about mathematics needs to be taught by a teacher passionate about mathematics.

Some interesting Hex links to investigate (links current as of Feb 2009):
Math Academy Platonic Realms
Mathworld
Thomas Maarup
Hexwiki
Hexwiki printable boards
Cut-the-knot

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Related posts:

1. Friday Afternoon Lifesavers – Math Videos from Bill Lombard – ppt