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I really enjoyed Camp Logic and am now reading another math book not geared toward teaching math. I am reading about the game of "Hex" created by Piet Hein. It has many versions and goes by other names as well. What I find interesting is that this book discusses how larger boards of Hex do not have known proven strategies (but on very small boards you can easily see how the first player can win with correct placement of their first piece). Winning strategies change with the shape of the board and I think this would be fun to explore in class along with the other strategy games in Camp Logic.

So my question is this... The book states that there is no formal proof or it's difficult to prove that the game cannot end in a draw. How can this be so? I think the book means that a mathmatical proof is difficult, but I think I can "see" a practical proof. If you try to fill a board up with two "colors" for two players, it is impossible to fill a board without creating chains. I'm looking at smaller boards and furthermore do not see a way to avoid forming a chain from one side to the other. It seems to me that you would need 4 colors/4 players to be able to fill the board without forming chains because each space touches 6 other spaces. Is this correct? Can it be related to map coloring? Can I show this in a class setting after playing the regular game? One neat variation of Hex is to force the other player to create a chain across the board. My students would be upper elementary/middle school.

The book is "Hexaflexagons, probability paradoxes, and the tower of Hanoi" by Martin Gardner. Thanks!

Comment

Maria Droujkova

**Answer** by Maria Droujkova , Make math your own, to make your own math
·
Jun 20, 2018 at 11:41 AM

Hello,

Glad you enjoyed Camp Logic! I passed your question on to the authors, and here is Mark Saul's reply:

~~~

The game of hex has not been completely solved. Here are two references to results already obtained:

http://mathworld.wolfram.com/GameofHex.html

https://en.wikipedia.org/wiki/Hex_(board_game)

Both cite many more references.

The writer is correct that the game must end, and cannot result in a draw. I’m not sure where she read anything to the contrary.

~~~

I hope this helps, either to address your plans or to formulate further questions for this discussion.

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