## Task 2 - 260622

The girls Britta, Petra, and Anja wish for a ball, a doll, and a stamp album.

Each of the girls wishes for exactly one of the mentioned items, and each girl wishes for a different item. Marie is supposed to find out which of the girls wishes for which item. In response to her question, she receives the following answers:

(1) Britta wishes for the ball.

(2) Petra does not wish for the ball.

(3) Anja does not wish for the album.

Of these three answers, exactly one is true, and the other two are false.

If one knows this, one can determine for each of the three girls which item she wishes for.

Explain how these determinations can be made and state the determinations!
We distinguish three cases, depending on which of the three answers is true:

1. Suppose answer (1) were true, and answers (2) and (3) were false. This case cannot occur, because then both Britta and Petra would wish for the ball.
2. Suppose answer (2) were true and answers (1) and (3) were false. This case cannot occur; because then neither Petra nor Britta would wish for the ball, nor would Anja (since she would wish for the album).

Therefore, the following case must apply:

3. Answer (3) is true, and answers (1) and (2) are false. That (2) is false means: Petra wishes for the ball (in agreement with (1) being false). Anja does not wish for the ball; and that (3) is true now means unequivocally: Anja wishes for the doll, Britta wishes for the album.