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Two sets with the same sum

Source: 1962 All-Soviet Union Olympiad

January 15, 2018
combinatoricsRussia

Problem Statement

Given are two sets of positive numbers with the same sum. The first set has mm numbers and the second nn. Prove that you can find a set of less than m+nm+n positive numbers which can be arranged to part fill an m×nm \times n array, so that the row and column sums are the two given sets.
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