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1-,0,1 on nxn table (II Soros Olympiad 1997-98 R3 10.8)

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June 6, 2024
combinatorics

Problem Statement

Is it possible to fill an n×nn \times n table with the numbers −1-1, 00 and 11 so that all 2n2n sums in each column and each row are different? Solve the problem with a) n=5n = 5; b) n=10n = 10.
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