8. (10 points) There is a $6 \times 6$ square, divided into 36 $1 \times 1$ squares. Select some of these $1 \times 1$ squares and draw their diagonals, such that no two drawn diagonals have a common point. What is the maximum number of diagonals that can be drawn? $\qquad$
8. (10 points) There is a $6 \times 6$ square, divided into 36 $1 \times 1$ squares. Select some of these $1 \times 1$ squares and draw their diagonals, such that no two diagonals have a common point. What is the maximum number of diagonals that can be drawn? $\qquad$ 

【Solution】Solution: As shown in the left figure, rows $a_{1}$ and $a_{2}$ can have at most 7 diagonals drawn (there are 7 points on $l_{1}$, and each diagonal must use one point).

Similarly: rows $a_{3}$ and $a_{4}$ can also have at most 7 diagonals drawn, and the same applies to rows $a_{5}$ and $a_{6}$.
Therefore, the maximum number of diagonals that can be drawn is $7 \times 3 = 21$.
Thus, the answer is 21.
The construction is shown in the right figure.