Some people familiar with the Go chess may know that in a traditional Go game,the players take turns placing the stones on the vacant points of a board. Once placed on the board, stones may not be moved, while stones are removed from the board if the stone or group of stones is surrounded by opposing stones on all orthogonally adjacent points, in which case the stone or group is captured.
Now we consider a variant of the game. A black stone is put on the center of an empty 19*19 Go board. Then the white player puts its white stone once on the vacant points of a board. Different from traditional rules, the black player will not put other black stones on the chessboard. Instead, he can move his unique stone at the intersection of the vacant horizontal and vertical lines on the chessboard at will. The player can move one square in any of the four directions at a time, as long as there is no white piece on the target point. When the black player moves one square, his opponent will take turns placing the white stones on the vacant points of a board, until the unique black stone is surrounded by white stones on all orthogonally adjacent points, in which case the black stone is captured. Then the question is:
- How many white stones at least are needed to capture the only black stone on the chessboard?
- What if the board is infinite?
