MathDB
Problem involving table

Source: Pre-VMO 2012 - Problem 4

November 27, 2011
combinatorics proposedcombinatorics

Problem Statement

For a table n×9n \times 9 (nn rows and 99 columns), determine the maximum of nn that we can write one number in the set {1,2,...,9}\left\{ {1,2,...,9} \right\} in each cell such that these conditions are satisfied:
1. Each row contains enough 99 numbers of the set {1,2,...,9}\left\{ {1,2,...,9} \right\}.
2. Any two rows are distinct.
3. For any two rows, we can find at least one column such that the two intersecting cells between it and the two rows contain the same number.
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