Coloring unit squares
Combinatorics · proposed by @vipproaccout
Consider a $2 \times 4$ grid consisting of $8$ unit squares. Using $4$ different colors, color the $8$ squares so that each square receives exactly one color. How many colorings are there such that, among all pairs of squares sharing a common side, exactly one pair has the same color, while every other pair of adjacent squares has different colors?