1993 Putnam A4

Let $x_1, x_2, \dots, x_{19}$ be positive integers each of

which is less than or equal to 93. Let $y_1, y_2, \dots, y_{93}$ be

positive integers each of which is less than or equal to 19. Prove that

there exists a (nonempty) sum of some $x_i$'s equal to a sum of some $y_j$'s.

令 $x_1, x_2, \dots, x_{19}$ 分别为正整数

小于或等于 93。令 $y_1, y_2, \dots, y_{93}$ 为

小于或等于 19 的正整数。证明

存在一些 $x_i$ 的(非空)总和等于一些 $y_j$ 的总和。