8.60 What is the maximum number of "rooks" that can be placed on a $3 n \times 3 n$ chessboard such that each rook is attacked by at most one other rook?
[Solution] Take $n$ $3 \times 3$ squares arranged along the main diagonal on the chessboard, and place 1 "rook" in each of the 4 shaded cells in each square, then there are $4 n$ rooks on the chessboard (as shown in the figure), and each rook is attacked by exactly one other rook. It is clear that the maximum value is no less than $4 n$.

On the other hand, assume that each rook on the chessboard is attacked by at most one other rook. If a rook is not attacked by any other rook, then it occupies a unique row and column of the chessboard, meaning there are no other rooks in its row or column. If rook $A$ is attacked by rook $B$, then rook $B$ is also attacked by rook $A$, and neither is attacked by any other rook. Therefore, the two rooks occupy 2 rows and 1 column or 1 row and 2 columns. Since the chessboard has $3 n$ rows and $3 n$ columns, at most $4 n$ rooks can be placed.
In summary, the maximum number of rooks that can be placed on the chessboard is $4 n$.