## Task 1 - 181211

At the Mathematics Olympiad, three students meet. "Have you noticed," one of them, a girl, asks, that we are called Long, Fat, and Thin, and that exactly one of us is exceptionally tall, another is notably fat, and the third is alarmingly thin?"

"Yes, indeed," replies another, the thin student, "but none of us has a name that matches the characteristic that describes the respective student." "You are absolutely right!" agrees the student named Long.

According to this, what is the name of the tall student, the name of the fat student, and the name of the thin student, given that the girl who asked the question is not fat? Which of the characteristic traits and which name does the girl have?
The thin student (according to his statement) does not have the name Dünn, and he is different from the student named Lang, who agrees with him; therefore, he is called Dick.

Thus, the tall student is not called Dick; and since he also does not bear the name Lang, he is called Dünn. Consequently, the name Lang remains for the fat student.

The girl is different from the thin student who disagrees with her, furthermore, she is not fat by assumption; therefore, she is the tall student named Dünn.

Note: The attempt to directly and solely conclude that the girl cannot be called Lang because the student Lang agrees with the student who disagrees with the girl, cannot be considered correct.

## Adopted from $[5]$