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I don't know how

 

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?

 Feb 20, 2023
 #1
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this question is easy if you draw the squares out, 5 squares, 

(  )  (  )  (  )  (  )  (  )

at least 3 have to be red and no square next to each other can be red so the only way to place this is 

(R)  (  ) (R)  (  )  (R)  

Now there are only 2 colors left for each box, Yellow or Blue

(R) (Y) (R) (Y) (R)
(R) (B) (R) (B) (R)
(R) (Y) (R) (B) (R)
(R) (B) (R) (B) (R)

you obviously don't have to write them all out, but I did to show you.  2 colors in each of the left over squares can be inputted, answer is 2x2 which is 4

 Feb 21, 2023

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