Task 1 - 250721 Annett, Birgit, and Cornelia performed differently in the last class test; one of these students received a grade of 1, another a grade of 2, and the third a grade of 3.

Kerstin, a classmate, tells at home: "Annett did not get a 1, Birgit did not get a 2, but Cornelia got a 2."

It turns out, however, that Kerstin was wrong in exactly two of these three statements.

Can the grades of the individual students be determined uniquely from these statements? If this is the case, provide the grade distribution!
If Kerstin's first and second statements were false and the third true, Birgit and Cornelia would have a 2, which contradicts the condition that the three students have different grades.

If Kerstin's first and third statements were false and the second true, then Annett would have a 1, and Birgit and Cornelia would not have a 2, which contradicts the condition that the grade 2 was awarded.

This leaves only the possibility: Kerstin's second and third statements are false, and the first statement is true.

This leads to the grade distribution: Birgit 2, Annett (therefore not 2 and also not) 1, so Annett 3; and consequently Cornelia 1. Thus, the grades are uniquely determined.