HMMT-Feb 2023 guts, Problem 36

After the Guts round ends, the HMMT organizers will calculate $A$, the total number of points earned over all participating teams on questions 33, 34, and 35 of this round (that is, the other estimation questions). Estimate $A$. Submit a positive integer $E$. You will receive $\max (0,25-3 \cdot|E-A|)$ points. (If you do not submit a positive integer, you will receive zero points for this question.) For your information, there are about 70 teams competing.

Solution: Solution: Only 8 teams scored a positive number of combined points on questions 33, 34, and 35 . A total of 3 points were scored on question 33, 6 points on question 34 , and 4 points on question 35. Extended results can be found in our archive. $\fbox{13}$.

Answer: 13