2024 AMC 8 Problem 7

A 3 \times 7 rectangle is covered without overlap by 3 shapes of tiles: 2 \times 2, 1 \times 4, and 1 \times 1, shown below. What is the minimum possible number of 1 \times 1 tiles used?

\textbf{(A)} 1 \qquad \textbf{(B)} 2 \qquad \textbf{(C)} 3 \qquad \textbf{(D)} 4 \qquad \textbf{(E)} 5

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