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Thought about the following while in a Complex Analysis lecture:

Let there be a $N \times N$ grid of squares and two players $A$ and $B$. First, $A$ needs to draw a line $l$ that needs to intersect the grid; then, $B$ has to select a square cut by $l$ and remove it from the grid; then, $B$ has to draw a line intersecting the grid but which doesn't cut the previously removed square, and so on ($A$ has to remove a square cut by the previous line and draw a new line intersecting the grid but not cutting the previously removed squares etc). The loser is the the one can't draw any more lines. Is there a winning strategies for some player? Find it.

I just did the small cases $N=2$ and $N=3$ manually and got that the answer is yes.

Any imput is welcome!

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Thought about the following while in a Complex Analysis lecture:

Let there be a $N \times N$ grid of squares and two players $A$ and $B$. First, $A$ needs to draw a line $l$ that needs to intersect the grid; then, $B$ has to select a square cut by $l$ and remove it from the grid; then, $A$ B$has to draw a line intersecting the grid but which doesn't cut the previously removed square, and so on ($BA$has to remove a square cut by the previous line and draw a new line intersecting the grid but not cutting the previously removed squares etc). The loser is the the one can't draw any more lines. Is there a winning strategies for some player? I just did the small cases$N=2$and$N=3$manually and got that the answer is yes. Any imput is welcome! 3 deleted 1 characters in body Thought about the following while in a Complex Analysis lecture: Let there be a$N \times N$grid of squares and two players$A$and$B$. First,$A$needs to draw a line$l$that needs to intersect the grid; then,$B$has to select a square cut by$l$and remove it from the grid; then,$A$has to draw a line intersecting the grid but which doesn't cut the previously removed square, and so on ($B$has to remove a square cut by the previous line and draw a new line intersecting the grid but not cutting the previously removed squares etc). The loser is the the one can't draw any more lines. Is there a winning strategies for some player? I just did the small cases$N=2$and$N=3\$ manually and got that the answer is yes.

Any imput is welcomedwelcome!