ISL 1988 Problem 73

A two-person game is played with nine boxes arranged in a $3 \times 3$ square and with white and black stones. At each move a player puts three stones, not necessarily of the same colour, in three boxes in either a horizontal or a vertical line. No box can contain stones of different colours: if, for instance, a player puts a white stone in a box containing black stones the white stone and one of the black stones are removed from the box. The game is over when the centrebox and the cornerboxes contain one black stone and the other boxes are empty. At one stage of a game $x$ boxes contained one black stone each and the other boxes were empty. Determine all possible values for $x.$