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4 colors in 5x5 board - All-Russian MO 2001 Regional (R4) 8.7

Source:

September 25, 2024
combinatoricsColoring

Problem Statement

Is it possible to paint the cells of a 5×55\times 5 board in 44 colors so that the cells standing at the intersection of any two rows and any two columns were painted in at least 3 3 colors?
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