Problem 5.5. Several schoolchildren have enrolled in math circles. They want to distribute them into groups evenly - so that the number of students in any two groups differs by no more than 1.

As a result of such even distribution, 6 groups were formed, among which exactly 4 groups have 13 students each. How many schoolchildren could there be in total? List all possible options.
Answer: 76 or 80.

Solution. Since the number of students in the groups differs by no more than 1, the remaining two groups can have either 12 or 14 students each (it is clear that groups of 12 and 14 students cannot exist simultaneously). Therefore, the total number of students can be $13 \cdot 4 + 12 \cdot 2 = 76$ or $13 \cdot 4 + 14 \cdot 2 = 80$.