the 10 X 20 lattice game has the following rules:(adsbygoogle = window.adsbygoogle || []).push({});

- 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).

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# Game theory, need help

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