Question

Школьники Александр, Борис, Сергей, Дарья и Елена с понедельника по пятницу посещали занятия хора. Известно, что: ов каждый из пяти дней ровно трое из школьников присутствовали, а ровно двое отсутствовали; • никто из школьников не отсутствовал два дня подряд и никто не присутствовал три дня подряд; • Александр пропустил на два дня больше, чем Сергей; • был только один день, когда Борис и Дарья одновременно были на занятии; • в понедельник Дарья была на занятии. Кто из школьников был на занятии в пятницу?​

Answer 1

Пошаговое объяснение:

Сергей был на занятиях в пятницу

Answer 2

Problem Analysis

We are given the following information about five students (Alexander, Boris, Sergey, Daria, and Elena) attending choir classes from Monday to Friday: - Each day, exactly three students were present, and exactly two students were absent. - No student was absent for two consecutive days, and no student attended for three consecutive days. - Alexander missed two days more than Sergey. - There was only one day when Boris and Daria were present together. - Daria attended on Monday.

We need to determine which students were present on Friday.

Solution

Let's analyze the given information step by step to find out which students were present on Friday.

1. Each day, exactly three students were present, and exactly two students were absent. This means that the total number of students is five, and each day, three students attended while two students were absent.

2. No student was absent for two consecutive days, and no student attended for three consecutive days. This means that no student can be absent for two days in a row, and no student can attend for three days in a row.

3. Alexander missed two days more than Sergey. This implies that Alexander missed two days more than Sergey, but we don't know the exact number of days missed by each student.

4. There was only one day when Boris and Daria were present together. This means that Boris and Daria attended together on one day, but we don't know which day it was.

5. Daria attended on Monday. This means that Daria attended on Monday, and we need to determine which students were present on Friday.

Let's analyze the information further to find a solution.

Based on the given information, we can make the following observations:

- Since each day, three students attended and two were absent, we can conclude that each student attended three days and was absent two days. - Since no student can be absent for two consecutive days, we can conclude that each student must have attended on at least one of the two consecutive days. - Since no student can attend for three consecutive days, we can conclude that each student must have been absent on at least one of the three consecutive days.

Let's consider the attendance of each student day by day:

- Monday: Daria attended. We don't know the attendance of other students on this day. - Tuesday: Since no student can be absent for two consecutive days, Daria cannot attend on this day. We don't know the attendance of other students on this day. - Wednesday: Since no student can attend for three consecutive days, Daria cannot attend on this day. We don't know the attendance of other students on this day. - Thursday: Since no student can attend for three consecutive days, Daria cannot attend on this day. We don't know the attendance of other students on this day. - Friday: We need to determine which students were present on this day.

Based on the given information, we know that exactly three students attended each day. Since Daria attended on Monday, she must have been absent on Tuesday, Wednesday, and Thursday. Therefore, Daria cannot be one of the students attending on Friday.

Let's consider the attendance of the remaining four students (Alexander, Boris, Sergey, and Elena) on Friday:

- Alexander: Since Alexander missed two days more than Sergey, and Daria missed three consecutive days, Alexander cannot be one of the students attending on Friday. Otherwise, he would have attended for three consecutive days (Wednesday, Thursday, and Friday), which is not allowed. - Boris: We know that Boris and Daria were present together on one day. Since Daria was absent on Tuesday, Wednesday, and Thursday, Boris cannot be one of the students attending on Friday. Otherwise, he would have attended for three consecutive days (Tuesday, Wednesday, and Friday), which is not allowed. - Sergey: Since Alexander missed two days more than Sergey, and Daria missed three consecutive days, Sergey cannot be one of the students attending on Friday. Otherwise, he would have attended for three consecutive days (Wednesday, Thursday, and Friday), which is not allowed. - Elena: Since we have eliminated all other students, Elena must be one of the students attending on Friday.

Therefore, the only student who could have attended on Friday is Elena.

Conclusion

Based on the given information, the only student who was present on Friday is Elena.

Please note that this solution is based on the given information and the logical deductions made from it. If there is any additional information or clarification needed, please let me know.