MathDB

Josie and Ross are playing a game on a

20 \times 20

chessboard. Initially the chessboard is empty. The two players alternately take turns, with Josie going first. On Josie’s turn, she selects any two different empty cells, and places one white stone in each of them. On Ross’ turn, he chooses any one white stone currently on the board, and replaces it with a black stone. If at any time there are

8

consecutive cells in a line (horizontally or vertically) all of which contain a white stone, Josie wins. Is it possible that Ross can stop Josie winning - regardless of how Josie plays?

Problem Statement