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edited Nov 23 2011 at 3:32

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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edited Nov 23 2011 at 2:17

Cosmin Pohoata
466●1●8

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 ($B$ $A$ 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?

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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edited Nov 23 2011 at 1:12

Cosmin Pohoata
466●1●8

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!