2017 Putnam A4

A class with $2N$ students took a quiz, on which the possible scores were $0,1,\dots,10$. Each of these scores

occurred at least once, and the average score was exactly $7.4$. Show that the class can be divided into two groups of $N$ students in such a way that the average score for each group was exactly $7.4$.

一个由 $2N$ 学生组成的班级进行了一次测验，可能的分数为 $0,1,\dots,10$。这些分数中的每一个

至少发生过一次，平均得分恰好为 7.4 美元。证明班级可以分为两组，每组学生人数为 $N$，每组的平均成绩恰好为 $7.4$。