15. On an $8 \times 8$ square grid of a chessboard, some squares are marked with stars, such that:
(1) No two starred squares share a common edge or vertex;
(2) Every unstarred square shares a common edge or vertex with at least one starred square.
What is the minimum number of squares that need to be starred? Explain your reasoning.
(1990 Chinese National Training Team Practice Problem)
15. The figure below is marked with 9 asterisks, which clearly meets the requirements of the question. In the figure, 9 check marks “ $\sqrt{ }$ ” are marked, and no matter which square on the chessboard is marked with an asterisk, it can share at most one side or corner with one of these 9 squares. Therefore, to meet the requirements of the question, at least 9 squares must be marked with asterisks. In summary, to meet the requirements of the question, the minimum number of asterisks to be marked is 9.