56 (979). After writing the test, the students Volodya, Sasha, and Petya reported at home:

Volodya: “I got a ‘5’.”

Sasha: “I got a ‘3’.”

Petya: “I did not get a ‘5’.”

After the test was checked, it turned out that one of the boys received a ‘4’, another a ‘3’, and the third a ‘5’. What grade did each receive, given that two of them correctly named their grade, and one was wrong?
Solution. If Vovochka had made a mistake (received not "5"), and the others had correctly named their grades, then Sasha would have received "3", Petya - "4". It turns out that Vovochka received the same grade as Sasha or Petya, which contradicts the condition of the problem: all received different grades. Therefore, Vovochka did not make a mistake. If Petya had made a mistake, then he would have received the same grade as Vovochka (which contradicts the condition of the problem). Therefore, Petya could not have made a mistake: he received "3" or "4". It remains to accept that Sasha made a mistake and, accordingly, he received "4", Vovochka - "5", Petya - "3".