5.2. Anya lies on Tuesdays, Wednesdays, and Thursdays and tells the truth on all other days of the week. Vanya lies on Thursdays, Fridays, and Saturdays and tells the truth on all other days of the week. When asked: "What day of the week is it today?" Anya answered: "Friday," and Vanya - "Tuesday." On which days of the week could this have happened? Explain your answer.
Answer: Tuesday, Thursday, or Friday. Both cannot be telling the truth as they name different days. If Anya is telling the truth, then it is Friday; if Vanya is telling the truth, then it is Tuesday. Another possibility is that both are lying, in which case the day is Thursday.

Comment. Only the answer without explanations - 3 points; incomplete answer (Thursday missed) - 1 point. Incomplete answer with explanations - 3 points.