A rectangular flag is made up of 5 vertical stripes, as shown in the picture below. The stripes of this flag will be painted, one in each color, with the colors: blue, red or green. The number of different ways this flag can be painted, with the restriction that no two consecutive stripes are painted the same color, is:
Let's first to make fast of resolve replace colour names by number so 1, 2, 3
I did for the 1 because this could be used as the same for the other numbers, so you multiply by 3 all the possibilities that could just for the 1, I have to say that I didn't need finishes the possibilities when I be in the 3rd house I already notice that the padron is multiply by 2 each more houses so this way you can discover even for 600 houses, just seeing the padron and making a formula is to cry think but I gonna say what is the formula
If I only have 3 options the possibilities are for the first number 3, but for the second, just 2 because can't be repeated and for the 3rd also 2 because can't be the number before, and for the 4th multiply by 2 because can't be the number before just the same and for the 5th only 2 for the same reason. And there in the site is that way becuase is look blink, and there the formula, see isn't automatic the person have to test to see how works.
Rute Bezerra de Menezes Gondim
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