3. (8 points) In the final math exam of Class 1, Grade 3, the top 10 scores form an arithmetic sequence. It is known that the full score is 100 points, and each student's score is an integer. The 3rd, 4th, 5th, and 6th place students scored a total of 354 points. Given that Xiao Yue scored 96 points, how many points did the 10th place student score?
【Solution】Solution: Let the 10th student scored $a$ points, and the scores of the top 10 students form an arithmetic sequence with a common difference of $d$. Then the 3rd, 4th, 5th, and 6th students scored $a+7d$, $a+6d$, $a+5d$, and $a+4d$ respectively,

The total score of the 3rd, 4th, 5th, and 6th students is:
$$
(a+7d)+(a+6d)+(a+5d)+(a+4d)=4a+22d=354,
$$

Rearranging, we get $2a+11d=177 \cdots$ (1), Let Xiao Yue ranked $m$th, then $1 \leqslant m \leqslant 10$, then $a+(10-m)d=96 \cdots(2)$,
(2) $\times 2$ - (1), we get $(9-2m)d=15$,
(1) When $9-2m=3, d=5$, we get $\left\{\begin{array}{l}m=3 \\ d=5\end{array}\right.$, at this time $a=61$;
(2) When $9-2m=5, d=3$, we get $\left\{\begin{array}{l}m=2 \\ d=3\end{array}\right.$, at this time $a=72$;
(3) When $9-2m=1, d=15$, we get $\left\{\begin{array}{l}m=4 \\ d=15\end{array}\right.$,
At this time, Xiao Yue ranked 4th, the 3rd place scored $96+15=111$ (points), because $111>100$, so it does not meet the requirements;

In summary, the 10th student scored 61 points or 72 points.
Answer: The 10th student scored 61 points or 72 points.