Math Is Fun Forum

Agnishom

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From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,974

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Beautiful Proof for non-drawablity of Hex

Imagine the playing board for the game of Hex to be made out of paper. Whenever red moves, he colors the hexagon of his choice red. Whenever blue moves, he cuts out the hexagon of his choice. Repeat this until no one can move any more.

Pick up the playing board in your hands, holding the two 'red' edges. Pull your hands apart. Either the paper stops you, in which case there must be a path of red squares and so red wins; or nothing stops you, in which case there is a 'path' of cut out squares between the top and the bottom of the board, and so blue wins.

Clearly, one of the two must occur; and so someone must win.

Kind of sounds like Jordan Curve theorem

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.