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numbers 0-2 in nxn board (IV Soros Olympiad 1997-98 Correspondence 9.5)

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June 1, 2024
combinatorics

Problem Statement

There is a square table with side nn. Is it possible to enter the numbers 00, 11 or 22 into the cells of this table so that all sums of numbers in rows and columns are different and take values from 11 to 2n2n, if: a) n=7n = 7 ? b) n=8n = 8 ?
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