The box below forms a basis for a game between two players. The idea is that the two players take turns shading in one of the six rectangles (numbered 1 through 6) with one of two colors- say red or blue.

+-+---+------------+
| |   |            |
| | 2 |     3      |
| |   |            |
| +---+--------+---+
|1|            |   |
| |     6      | 4 |
| |            +---+
| |            | 5 |
+-+------------+---+

Either player can use either color on any turn. It is illegal to shade a rectangle with a color that has already been given to a neighboring rectangle. If you don't have a legal move at your turn, you lose the game.

Prove that for each opening move by the first player, the second player can always win.

(In reply to Move-counter move by Jer)

This doesn't specify which color is being played each time.

Remember that each player chooses the color independently on each turn and need not stick to one color.

Posted by Charlie on 2013-05-02 14:41:26