$36 \cdot 36$ As shown, on a $4 \times 6$ billiard table, there are two balls $P$ and $Q$. If ball $P$ bounces off the edges $A B, B C, C D$ and $D A$ in sequence, and then hits ball $Q$ exactly. Then when ball $P$ is hit, the aim should be at (where $A_{k}$ are the six equal division points on $A B$)
(A) $A_{2}$.
(B) $A_{3}$.
(C) $A_{4}$.
(D) $A_{5}$.
(Chinese Jiangsu Province Junior High School Mathematics Competition, 1989)
[Solution 1] Using the conclusion that the angle of incidence equals the angle of reflection, it is not difficult to deduce the path of the ball $P$ after being hit (as shown in the left lower diagram): $P \rightarrow A_{3} \rightarrow B^{\prime} \rightarrow C^{\prime} \rightarrow D^{\prime}$.
Therefore, the answer is $(B)$.
[Solution 2] If the table is reflected four times as shown in the upper right diagram, then connecting the starting point and the reflected points of the two tables, $P$ and $Q$ (as indicated by the dashed line in the diagram), gives the path of the ball $P$ after it hits each side of the table and reaches $Q$.
Similarly, $A_{3}$ can be found.
Therefore, the answer is $(B)$.