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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?

 Nov 4, 2022
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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?  

 

Since you must have three red squares, and none of them can touch each other,  

then the red squares can be only in squares 1, 3, and 5. 

 

That leaves two squares to contend with, squares 2 and 4.  

You can fill those two squares 4 ways, as follows:    

 

Red   Yellow   Red   Blue   Red  

Red   Blue   Red   Yellow   Red  

Red   Yellow   Red   Yellow   Red  

Red   Blue   Red   Blue   Red  

.

 Nov 5, 2022

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