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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, and at lest three of the squares are red.  How many ways are there to color the five squares?

 Jan 1, 2023
 #1
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There are 14 ways.

 Jan 1, 2023
 #2
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The first, last, and middle numbers must be red. 

 

This means that the 2nd and 4th squares can be either yellow or blue. There are 2 options for each which makes for \(2 \times 2 = \color{brown}\boxed{4}\) cases

 Jan 1, 2023

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