## Task 1 - 170821

Four students, Anja, Birgit, Christoph, and Dirk, played the following game, whose rules were known to all of them:

One of them, for example, Dirk, leaves the room. Now, one of the people, Anja, Birgit, or Christoph, takes a predetermined object, such as a thimble, and Dirk is called back in. He then receives statements from the other players, with the exact one who has the thimble making a false statement.

In one execution of this game, the statements were as follows:

Anja: I do not have the thimble, and Christoph has the thimble.

Birgit: Anja has the thimble, and I do not have the thimble.

Christoph: I do not have the thimble.

Investigate whether it can be conclusively determined from these statements which player took the thimble! If this is the case, identify this player!
(1) If Christoph had the thimble, then Birgit's statement would be false, contradicting the game rules. Therefore, Christoph does not have the thimble.

(2) If Birgit had the thimble, then Anja's statement would be false, contradicting the game rules. Therefore, Birgit does not have the thimble either.

(3) Consequently, only Anja can have the thimble. In fact, Anja's statement would then be false, and the statements of Birgit and Christoph would be true.

Thus, it is definitively established that Anja took the thimble.