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In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the five squares, if there must be at least three yellow squares?

 May 4, 2024
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Because no two consecutive squares can have the same color, to have at least three yellow squares, they must be placed in squares 1, 3, and 5.

 

The remaining squares, 2 and 4, must then be colored red and blue in some order. There are 2!=2 ways to order these remaining colors, so there are 2​ total colorings.

 May 4, 2024

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