## Task 6 - 030936

In a game, three students, Anna, Brigitte, and Claudia, each hide an object in their handbags, namely a ball, a pencil, and a pair of scissors. Dieter is supposed to figure out who has the ball, who has the pencil, and who has the scissors.

In response to his questions, he receives the following answers, of which only one is true, while the other two are false:

(1) Anna has the ball.

(2) Brigitte does not have the ball.

(3) Claudia does not have the scissors.

Who has the ball, who has the pencil, and who has the scissors?
1. Case: If the 1st statement is correct, then Anna has the ball. Therefore, Brigitte cannot have the ball, which means the 2nd statement is also true. This, however, contradicts the agreement.

Thus, the assumption that the 1st statement is true is false.

2. Case: If the 2nd statement is correct, then Brigitte does not have the ball. According to the agreement, the other two statements must be false, so their negations must be true: Anna does not have the ball, and Claudia has the scissors.

If neither Anna nor Brigitte has the ball, Claudia must have it, which contradicts the statement that Claudia has the scissors. Therefore, the 2nd assumption is also false.

3. Case: If the 3rd statement is correct, then Claudia does not have the scissors. Now, the 1st and 2nd statements must be negated to be true: Anna does not have the ball. Brigitte has the ball.

This means Anna has the scissors and Claudia has the pencil. There is no contradiction in this scenario, so this case is the solution.