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Let , , be positive integers such that . Alice and Bob play a game on an (initially uncoloured) grid as follows:
- First, Alice paints cells green.
- Then, Bob paints other (i.e.uncoloured) cells blue.
Alice wins if she can find a path of non-blue cells starting with the bottom left cell and ending with the top right cell (where a path is a sequence of cells such that any two consecutive ones have a common side), otherwise Bob wins. Determine, in terms of , and , who has a winning strategy.
- First, Alice paints cells green.
- Then, Bob paints other (i.e.uncoloured) cells blue.
Alice wins if she can find a path of non-blue cells starting with the bottom left cell and ending with the top right cell (where a path is a sequence of cells such that any two consecutive ones have a common side), otherwise Bob wins. Determine, in terms of , and , who has a winning strategy.