Question 9
The positive integers $a_1$, $a_2$, ..., $a_m$, $b_1$, $b_2$, ..., $b_n$ satisfy: $a_1 + a_2 + \ldots + a_m = b_1 + b_2 + \ldots + b_n \lt mn$. Show that we can delete some (but not all) of the numbers so that the sum of the remaining $a$'s equals the sum of the remaining $b$'s.