## Task 4 - 010834

Who has the ring?

Ruth, Fritz, Ewald, Brigitte, and Erika are playing a game of tag. Ruth leaves the room; in the meantime, one of the other children hides a ring on themselves. Ruth returns and must determine who has the ring. Each child then makes three statements. Of these statements, two are true and one is false. Ruth must determine who has the ring based on these statements without guessing.

Ewald: 1. I do not have the ring.

2. Fritz has the ring.
3. I have played this game many times before.

Fritz: 1. I do not have the ring.

2. Ewald is wrong if he thinks I have the ring.
3. Erika has the ring.

Now Ruth interrupts and says, "I need to think, maybe I can already figure out who has the ring." And after a few minutes, Ruth says who has the ring. How could she have figured it out?
The idea is to find out which statements of Ewald and Fritz contradict each other, as then one of them must be false.

Since Fritz's statements 1 and 2 are equivalent, they can only be true or false at the same time. The latter is excluded, as Fritz only makes one false statement. Therefore, his 3rd statement is false; neither he nor Erika have the ring.

Ewald's 2nd statement contradicts Fritz's first (which is true), so it is false.

Thus, Ewald's 1st statement must be true, leaving only Brigitte. Therefore, she has the ring.