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Minimum Zeros in Row Column Sum Table

2050SpecialistLinear AlgebraCombinatorics

1 Autumn tournament

An integer is written in each of the fields of a $9 \times 9$ square table. For every $k$ numbers in the same row (column), their sum is in the same row (column). Find the smallest possible number of zeros in the table if: a) $k = 5$; b) $k = 8$.
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