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Part of 2022 South East Mathematical Olympiad

Problems(1)

ways of painting

Source: 2022 China Southeast Grade 10 P4

m,n\geq 2

.Paint each cell of a

m\times n

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red or blue so that:for any two red cells in a row,one of the two columns they belong to is all red,and the other column has at least one blue cell in it.Find the number of ways to paint

S