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, 2019

Combinatorics Difficulty 6.0 National Olympiad Find the answer Hungary

A $k\times k$ array contains each of the numbers $1,2,\ldots,m$ exactly once, with the remaining entries all zero. Suppose that all the row sums and column sums are equal. What is the smallest possible value of $m$ if $k=3^n$ ( $n\in\mathbb{N^+}$ )?

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