Question 49
Anna and Bob play a game on the set of all points of the form $(m, n)$ where $m, n$ are integers with $|m|, |n| \leq 2019$. Let us call the lines $x = \pm 2019$ and $y = \pm 2019$ the *boundary lines* of the game. The points of these lines are called the *boundary points*. The *neighbours* of point $(m, n)$ are the points $(m+1, n)$, $(m-1, n)$, $(m, n+1)$, $(m, n-1)$.
Anna starts with a token at the origin $(0, 0)$. With Bob playing first, they alternately perform the following steps: At his turn, Bob deletes two points on each boundary line. On her turn Anna makes a sequence of three moves of the token, where a *move* of the token consists of picking up the token from its current position and placing it in one of its neighbours.
To win the game Anna must place her token on a boundary point before it is deleted by Bob. Does Anna have a winning strategy?
[Note: At every turn except perhaps her last, Anna **must** make **exactly** three moves.]
Anna starts with a token at the origin $(0, 0)$. With Bob playing first, they alternately perform the following steps: At his turn, Bob deletes two points on each boundary line. On her turn Anna makes a sequence of three moves of the token, where a *move* of the token consists of picking up the token from its current position and placing it in one of its neighbours.
To win the game Anna must place her token on a boundary point before it is deleted by Bob. Does Anna have a winning strategy?
[Note: At every turn except perhaps her last, Anna **must** make **exactly** three moves.]