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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