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?

Icebulb2 Oct 13, 2023

#3**+2 **

To color the five squares without any two consecutive squares having the same color, follow these steps:

1. Pick any color for the first square (3 choices: red, yellow, or blue).

2. Choose a different color for the second square (2 choices remaining).

3. Select a different color for the third square (2 choices remaining).

4. Choose a different color for the fourth square (2 choices remaining).

5. Lastly, pick a different color for the fifth square (2 choices remaining).

Multiply these choices together: 3 * 2 * 2 * 2 * 2 = 48 different ways to color the five squares.

WaterPheonix Oct 16, 2023