11.1. When composing the options for the district mathematics olympiad for grades $7, 8, 9, 10, 11$, the jury aims to ensure that in the option for each grade, there are exactly 7 problems, of which exactly 4 do not appear in any other option. What is the maximum number of problems that can be included in the olympiad?
Answer: 27.

Solution. The number of non-repeating tasks will be 20, the number of repeating tasks does not exceed $3 \cdot 5 / 2<8$. We will provide an example of variants with exactly 7 repeating tasks: 7th grade: $1,2,3$; 8th grade: $1,2,3$; 9th grade: $4,5,6$; 10th grade: $4,5,7$; 11th grade: $4,6,7$.