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Grid Five Color Maximum Coverage

2175ExpertCombinatoricsOptimization

PRÉPARATION OLYMPIQUE FRANÇAISE DE MATHÉMATIQUES

We have five colors and a $99 \times 99$ grid. Some squares of the grid are colored with one of the five colors such that: - Each color appears the same number of times in the grid. - No row and no column contains squares of different colors. What is the largest possible number of squares that can be colored following these rules?
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