## Task 4 - 130514

In a school class, some Thälmann Pioneers work in the club of international friendship. When asked who among them works in the club's translation office, 7 raise their hands.

Then, they are asked who works in the club's country circle; this time, 6 raise their hands. It is also noted that 5 of the Pioneers are active in the club's young correspondents' circle. There are no other circles in this club besides these three.

Next, the question is asked who works in both the translation office and the country circle; this time, 4 of the Pioneers raise their hands. It is also determined that 3 of them work in both the translation office and the young correspondents' circle, and 2 of the Pioneers belong to both the country circle and the young correspondents' circle.

Exactly one of the Pioneers from the mentioned school class belongs to all three circles.

Determine the total number of Pioneers from this class who work in the club of international friendship! (All numerical data are considered exact)
If the number of students in each circle is denoted by the initial letter of the circle, then \((d)=7\), \((l)=6\), and \(k=6\). Furthermore, in several circles, \((d+l)=4\), \((d+k)=3\), \((l+k)=2\), and \((d+k+l)=1\).

In \(d\) and \(l\) without \(k\), there are accordingly \((d+l)-(d+k+l): 4-1=3\) students, (*)

in \(l\) and \(k\) without \(d\), there are accordingly \((l+k)-(d+k+l): 2-1=1\) student, \(\left({ }^{* *}\right)\)

in \(k\) and \(d\) without \(l\), there are accordingly \((d+k)-(d+k+l): 3-1=2\) students. (***)

In \(d\) without \(k\) and \(l\), there are accordingly \((d)-(*)-(* *)-(* * *): 7-3-2-1=1\) student. Similarly, in \(l\) without \(k\) and \(d\), there is 1 student, and likewise in \(k\) without \(l\) and \(d\), there is 1 student.

In total, this results in \(1+1+1+3+1+2+1=10\).

Thus, 10 students in the class are working in the club of international friendship.

Solution taken from \([5]\)

### 2.14.2 II. Round 1973, Class 5