Counting

 

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?     

 

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

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

Then you put a different color in between them.     

 

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

to do it with. There are only four ways.    

 

Blue Blue     Yellow Yellow     Blue Yellow     Yellow Blue      

 

So, the answer is four ways.     

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