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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?

 Mar 24, 2024
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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?  

 

In order not to have two yellows next to each other,  

the three yellows must occupy squares 1, 3, and 5. 

 

That leaves squares 2 and 4 to fill, and two colors  

to do it with. There are only four ways. 

 

Blue Blue     Red Red     Blue Red     Red Blue  

 

So, the answer is four ways.  

.

 Mar 24, 2024

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