## Task 1 - 130721

The 36 students of a 7th grade class participate in extracurricular sports, each in exactly one of the sections Track and Field, Table Tennis, Swimming, Judo, and Chess. It is further known about the participation of the students in these sections:

(1) More than half practice Track and Field.

(2) More belong to the Swimming section than to the Table Tennis section.

(3) The sum of the number of members of the Chess section and the Judo section is exactly one ninth of all students.

(4) The number of students in the Table Tennis section is twice the number of students in the Chess section.

(5) The number of members in the Chess section is greater than double but less than four times the number of members in the Judo section.

Determine the number of students in each of the mentioned sections!
From (3) it follows that the sum of the number of chess players and the number of judo athletes is 4. Of all possible decompositions of the number 4 into two integer summands, only the one (5) where the number of chess players is 3 and the number of judo athletes is 1 is valid. This implies, according to (4), that exactly 6 students are members of the table tennis section.

According to (1), at least 19 students practice athletics, and according to (2), at least 7 students swim. Since only exactly 26 students remain for these two sports, 19 and 7 are the only possible numbers.

Thus, out of the 36 students, exactly 19 practice athletics, exactly 7 swim, exactly 6 play table tennis, exactly 3 play chess, and exactly 1 student practices judo.