Problem 7.4. On Monday, 5 people in the class received fives in math, on Tuesday, 8 people received fives, on Wednesday - 6 people, on Thursday - 4 people, on Friday - 9 people. No student received fives on two consecutive days. What is the minimum number of students that could have been in the class
Answer: 14.

Solution. Let's consider pairs of consecutive days.

- On Monday and Tuesday, 5s were received by $5+8=13$ people.
- On Tuesday and Wednesday, 5s were received by $8+6=14$ people.
- On Wednesday and Thursday, 5s were received by $6+4=10$ people.
- On Thursday and Friday, 5s were received by $4+9=13$ people.

Since no one could receive a 5 for two consecutive days, the number of students in the class is at least as large as the maximum of the obtained numbers. That is, there are at least 14 students in the class.

Let's provide an example of how fourteen students could receive 5s. We will number the children from 1 to 14.

- On Monday, 5s were received by students $10,11,12,13$ and 14.
- On Tuesday, 5s were received by students $1,2,3,4,5,6,7$ and 8.
- On Wednesday, 5s were received by students $9,10,11,12,13$ and 14.
- On Thursday, 5s were received by students $1,2,3$ and 4.
- On Friday, 5s were received by students $6,7,8,9,10,11,12,13$ and 14.