## Task 1 - 280721

In a mathematics class, students made the following statements about a natural number that lies between 100 and 200.

(1) André: "The number is divisible by 11."

(2) Birgit: "The number is a prime number."

(3) Christian: "The number is a composite number."

(4) Doris: "The number is a perfect square."

The mathematics teacher notes that exactly one of these four statements is false.

Investigate whether the number is uniquely determined by these findings! If this is the case, then give the number!
Since a prime number cannot be a composite number or a square number, statement (2) must be false, because otherwise (3) and (4) would be false, which would contradict the teacher's statement.

Due to this statement, (2) is the only false statement among (1) to (4), so (1) and (4) are true.

The number we are looking for is thus a square number divisible by 11. Since 11 is a prime number, this square number divisible by 11 must also be divisible by $11^{2}=121$. The only number divisible by 121 between 100 and 200 is 121 itself.

Thus, it is shown that the number we are looking for is uniquely determined; it is 121.