So, your first move would be to create an L, most sensibly by choosing (2,2), this leaves the L that is the left column and bottom row. From this point on, from this point on, whatever player 2 does, all player 1 needs to do is make sure that the number of clear squares across the bottom and up the side is equal after their turn.
In fact, I'm pretty sure they don't even need them to be equal, but I can't be bothered thinking of how to generalise it when keeping things equal would suffice.
Of you want I could give you an example to demonstrate if you still don't get it to explain the method.
Also wondering what a solution would be in higher dimensions.
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