Found problems: 1
2025 AIME, 3
Four unit squares form a $2 \times 2$ grid. Each of the $12$ unit line segments forming the sides of the squares is colored either red or blue in such way that each square has $2$ red sides and blue sides. One example is shown below (red is solid, blue is dashed). Find the number of such colorings.
[asy]
size(4cm);
defaultpen(linewidth(1.2));
draw((0, 0) -- (2, 0) -- (2, 1));
draw((0, 1) -- (1, 1) -- (1, 2) -- (2,2));
draw((0, 0) -- (0, 1), dotted);
draw((1, 0) -- (1, 1) -- (2, 1) -- (2, 2), dotted);
draw((0, 1) -- (0, 2) -- (1, 2), dotted);
[/asy]