7.4. Five friends gathered. The following conversation took place between them. Andrey: "I know a secret!". Borya (to Andrey): "You don't know!". Vitya: "Boris, you are wrong!". Gosha (to Vitya): "You are wrong, Vitya!". Dima: "You are lying, Gosha!". It is known that more than half of the boys told the truth. Does Andrey know the secret?
Answer: Andrey knows the secret.

Solution. Suppose Andrey lied. Then Borya told the truth, Vitya lied, Gosha told the truth, and Dima lied. This means that three out of five lied, which contradicts the condition. If Andrey told the truth, then Borya lied, Vitya told the truth, Gosha lied, and Dima told the truth, which meets the condition. Therefore, Andrey knew the secret.