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MathNet 2004 — Part 01 Question 65

Math Olympiad Vault · MathNet 2004 — Part 01

Question 65

In every cell of an $n \times n$ table one of the numbers $-1, 0$ and $1$ is written. Is it possible the sums of the numbers in every row and every column to be $2n$ mutually different numbers, if:


a) $n=4$;


b) $n=5$?