A game is played on a $23\times 23$ board. The first player controls two white chips which start in the bottom left and top right corners. The second player controls two black ones which start in bottom right and top left corners. The players move alternately. In each move, a player moves one of the chips under control to a square which shares a side with the square the chip is currently in. The first player wins if he can bring the white chips to squares which share a side with each other. Can the second player prevent the first player from winning?
Yes. Keep both black chips to occupy the opposite corners of the rectangle that the first player makes. Note that the first player won't be able to align their chips into a single row/column as long as the second player keeps following the above strategy, and additionally the first player must always break the rectangle where the second player can thus patch back with his move.
e.g. First player moves the bottom left chip one to the right. Second player thus keeps the rectangle, by moving the top left chip one to the right.
Since the first player can't even able to make the two chips align in the same row/column, he won't be able to get his chips adjacent to each other.
Shouldn't be mentioned that we cannot have two chips in the same square???
Because if we can the second player cannot prevent the first player from winning!