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Color black/white in 8*8 table

Source: 2016 Thailland October Camp 3.4

February 28, 2022
combinatoricsColoringcellstableconstruction

Problem Statement

The cells of a 8×88 \times 8 table are colored either black or white so that each row has a different number of black squares, and each column has a different number of black squares. What is the maximum number of pairs of adjacent cells of different colors?
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