13. (3 points) $A, B, C, D, E$ five boxes contain 9, 5, 3, 2, 1 balls respectively. The first student finds the box with the fewest balls, then takes 1 ball from each of the other boxes and puts it into this box. The second student finds the box with the fewest balls, then takes 1 ball from each of the other boxes and puts it into this box $\cdots$; after the 199th student has finished, $A, B, C, D, E$ five boxes will each have $\qquad$ balls, $\qquad$ balls, $\qquad$ balls, $\qquad$ balls, $\qquad$ balls.
【Solution】Solution: From the analysis, we know that the 8th child repeats with the 3rd, meaning a cycle of 5; thus, by analogy:
$$
\text { (199 - 2) } \div 5=39 \cdots 2 \text { (times); }
$$

The 199th student, after taking, should leave the five boxes $A, B, C, D, E$ with: 5, 6, 4, 3, 2 balls respectively; Answer: After 199 students have placed their balls, the five boxes $A, B, C, D, E$ will each contain $5, 6, 4, 3, 2$ balls.