Difference between revisions of "Draw"
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Revision as of 00:52, 18 December 2011
One of the beautiful properties of Hex is that the game can never end in a draw, i.e., there is always a winner.
There are various ways of proving this, for example:
- A proof by David Gale that used the fact that exactly three hexes meet at every vertex.
- An elegant proof using the game of Y.
- Another proof using the game of Y.
In fact, David Gale showed that the no-draw property is equivalent to the 2-dimensional case of Brouwer's fixed point theorem (a non-trivial theorem from topology saying that any continuous map from the unit square into itself must have a fixed point).
In 2006, Yasuhito Tanaka proved another equivalence involving Hex. The no-draw property is equivalent to the Arrow impossibility theorem.
