A1. The colors red, white, and blue are used to paint square tiles. Each tile is divided into a $2 \times 2$ grid of smaller squares, each of which can be painted one of the colors.

How many differently painted tiles can you get?

(Two tiles are considered the same if they can be rotated to look identical.

![](https://cdn.mathpix.com/cropped/2024_04_17_2582a2b087f6953c1edag-1.jpg?height=188&width=205&top_left_y=1502&top_left_x=1642)
A1. In total, there are 24 solutions. If we use only one color, there are 3 solutions. If we use two colors, we can choose a combination of two colors in three ways. With two colors, we can realize the following four possibilities:

In this case, that gives 12 possibilities.
![](https://cdn.mathpix.com/cropped/2024_04_17_7fa3f9281a1c56596c60g-1.jpg?height=152&width=822&top_left_y=546&top_left_x=867)

With all three colors, there must always be two squares of the same color. For each color choice for the two squares, there are three possibilities:

In this case, 9 possibilities.

In total, therefore, $3+12+9=24$
![](https://cdn.mathpix.com/cropped/2024_04_17_7fa3f9281a1c56596c60g-1.jpg?height=156&width=610&top_left_y=912&top_left_x=1042)