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?
I think I can solve this!
Let me start with what I am going to be writing out:
r = red
y = yellow
b = blue
|_| = one of the squares
So, we have
|_| |_| |_| |_| |_|
Since we need at least 3 red, there is only one way to do this:
|r|, |_|, |r|, |_|, |r|
Then the other two can be either yellow or blue and we have 2 * 2 ways to do this.
So, what I'm having is a total of 4 ways to color this square. (If you find any errors please let me know)