## A game of Hex

By David, 26 May 2015 Game

Try playing the game of Hex, and connect your sides of the board before your opponent cuts you off!

### You will need

Take turns marking a hexagon.

- Two different coloured pens or textas
- a printout of some hex boards
- An opponent to play against

### What to do

In Hex, you have to try and link two opposite sides of the board with your hexagons. Your opponent is trying to link the other two sides with their hexagons.

In this game, blue has won by linking the top and bottom of the board.

- Decide who is going to go first. The first player is trying to link the two white sides. The second player will try and link the two black sides.
- Taking turns, each player marks a hexagon as theirs using a pen. The white player can use empty circles, and the black player can use ’x’s. Any hexagon on the board can be marked so long as it hasn’t already been claimed.
- Once a hexagon has been marked, the other player cannot mark the same hexagon.
You can print the board out big, and use counters instead of drawing on the board.

- You win if you have connected your two sides with a path of hexagons that you have marked. When you have won, it will be impossible for your opponent to link their two sides.

If you like playing Hex, you could print a large hex board on A3 sized paper or draw a big copy of the board onto a sheet of cardboard. Then you can use counters instead of drawing on the board, and you can re-use it over and over.

### What’s happening?

Hex was invented by a mathematician named Piet Hein in 1942, and several years later, it was re-invented by another mathematician, John Nash. Both mathematicians were interested in using maths to study games. John Nash eventually won a Nobel Prize in Economics for his research into different games.

Many different mathematicians have proved the game can’t end in a draw – if the board fills up so that no one can play another piece, then one player must have won. John Nash used this fact to show that a perfect first player would always win, even against a perfect second player. However, John’s proof doesn’t actually tell you what the perfect strategy is.

Since the first player has an advantage, many Hex players start the game with a special first turn – the first player plays their first move, then the second player has the option to swap sides with the first player. If the start player plays a really good move then the second player will swap and have the advantage.

*If you’re after more maths activities for kids, subscribe to Double Helix magazine!*

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