There are 12 students in Mr. DoBa's math class. On the final exam, the average score of the top 3 students was 8 more than the average score of the other students, and the average score of the entire class was 85. Compute the average score of the top $3$ students.

[i]Proposed by Yifan Kang[/i]
1. Since the average score of the entire class of 12 students was 85, the sum of the scores of all the students is calculated as follows:
   \[
   12 \cdot 85 = 1020
   \]

2. Let the average score of the top 3 students be \( X \). Then, the sum of the scores of the top 3 students is:
   \[
   3X
   \]

3. The average score of the other 9 students is \( X - 8 \). Therefore, the sum of the scores of the other 9 students is:
   \[
   9(X - 8)
   \]

4. The sum of the scores of all 12 students is the sum of the scores of the top 3 students and the other 9 students:
   \[
   3X + 9(X - 8) = 1020
   \]

5. Simplify the equation:
   \[
   3X + 9X - 72 = 1020
   \]
   \[
   12X - 72 = 1020
   \]

6. Add 72 to both sides of the equation:
   \[
   12X = 1092
   \]

7. Divide both sides by 12 to solve for \( X \):
   \[
   X = \frac{1092}{12} = 91
   \]

The final answer is \( \boxed{91} \).