## Task 4 - 190614

Three pioneers from a school, Karin, Dieter, and Frank, were delegated to the district mathematics olympiad and won a first, a second, and a third prize (each of the three pioneers exactly one of these prizes). Later, Anette inquired about the performance of the three olympiad participants. She was told:

"Dieter did not receive the first prize." (1)

"Karin did not receive the second prize." (2)

"Frank received the second prize." (3)

Later, it turned out that exactly one of these three statements was true, while the others were false.

According to this, which of the three students received the first, which the second, and which the third prize?
Dieter did not receive a second prize; for if he had received a second prize, the 1st and 2nd statements would have been true.

Frank also did not receive a second prize; for if he had received a second prize, the 2nd and 3rd statements would have been true.

Therefore, Karin received a second prize. Thus, the 2nd and 3rd statements were false, while the first was true.

Consequently, Dieter, who could not have received either a first or a second prize, received a third prize. The first prize could ultimately only have been won by Frank; for the two remaining prizes had been obtained by Karin and Dieter.

Solutions of the 1st Round 1979 taken from [5]

### 3.20.2 2nd Round 1979, Class 6