A grid consists of all points of the form (m,n) where m and n are integers with ∣m∣≤2019,∣n∣≤2019 and ∣m∣+∣n∣<4038. We call the points (m,n) of the grid with either ∣m∣=2019 or ∣n∣=2019 the boundary points. The four lines x=±2019 and y=±2019 are called boundary lines. Two points in the grid are called neighbours if the distance between them is equal to 1.
Anna and Bob play a game on this grid.
Anna starts with a token at the point (0,0). They take turns, with Bob playing first.
1) On each of his turns. Bob deletes at most two boundary points on each boundary line.
2) On each of her turns. Anna makes exactly three steps , where a step consists of moving her token from its current point to any neighbouring point, which has not been deleted.
As soon as Anna places her token on some boundary point which has not been deleted, the game is over and Anna wins.
Does Anna have a winning strategy?Proposed by Demetres Christofides, Cyprus combinatoricswinning positionsgame strategygridlattice points