2026 AMC 8 Problem 20

The land of Catania uses gold coins and silver coins. Gold coins are 1 mm thick and silver coins are 3 mm thick. In how many ways can Taylor make a stack of coins that is 8 mm tall using any arrangement of gold and silver coins, assuming order matters?

\textbf{(A)} 3 \qquad \textbf{(B)} 7 \qquad \textbf{(C)} 10 \qquad \textbf{(D)} 13 \qquad \textbf{(E)} 16

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.