After the celebration, Mom put aside the last piece of cake for Aunt. When Aunt finally arrived, she found only a dirty plate instead of the treat. Mom tried to find out what happened and got the following answers from her four children:

Adam: "Blanka or Cyril ate it."

Blanka: "Adam or Cyril ate it."

Cyril: "None of us is lying."

Dana: "Everyone except me is lying."

In the end, it turned out that one of the children ate the cake and that this child was telling the truth.

Find out which child it was.

(E. Novotná)
The child who finished the cake spoke the truth.

Neither Adam nor Blanka could have finished the cake - otherwise, they couldn't claim that someone else did it.

If Cyril had finished the cake, then according to his statement, everyone, including Dana, would be telling the truth, which is contradictory - Cyril cannot be lying and telling the truth at the same time.

Therefore, Dana must have finished the cake - according to her statement, the other children were lying, and this does not lead to any contradiction as in the previous cases.

Evaluation. 2 points for excluding some possibilities (leading to a contradiction); 2 points for suspecting Dana (no contradiction); 2 points for completeness and quality of the comment.

Note. Be aware that we are only working with the implication "the child ate the cake, therefore spoke the truth." This can be replaced by, for example, "the child lied, therefore did not eat the cake," while thoughts like "the child did not eat the cake, therefore lied" are incorrect.