2. In a test, 25 students from eight schools participated. They correctly solved a total of 50 problems. Each student from the same school solved the same number of problems, while students from different schools solved a different number of problems. Each student correctly solved at least one problem. How many students solved only one problem?
Solution. Let's take one student from each school and assume that the first one solved 1 problem, the second one solved 2 problems, the third one solved 3, and so on, with the eighth one solving 8 problems. In this case, these 8 students solved a total of $1+2+3+4+5+6+7+8=36$ problems. Therefore, from our 22 students, 14 remain, and they solved a total of $50-36=14$ problems. According to this, each of these 14 students solved 1 problem. Finally, 15 students solved 1 problem.