the 10 X 20 lattice game has the following rules: - two players alternate picking points (x,y) in the plane. the points must have integer coordinates(lattice points) and we must have 1 ≤ x ≤ 10 1 ≤ y ≤ 20 - first player must begin from (1,1). that is, player 1 can choose any point with one coordinate or the other being 1. - if one player choose the point (x,y), then the next player must take a point of the form ( x,y' ), y' > y or ( x',y), x' > x. for example, player 2's first turn can be to choose (1,6) or (5,1), but not (2,3). - the winner is the player that chooses (10,20) > the first player has a winning strategy; that is, no matter what player 2 does, there is a reply by player 1 that will inevitably lead to victory. Hint (9, 19) is a winning position - a choice that guarantees an eventual win. Figure out why and work from there. find a winning strategy for player 1 and prove its correctness. Then, generalize this idea to any size of lattice ( Player 1 is not always the one who wins).