2017 AMC 10B Problem 6

What is the largest number of solid 2\text{ in.} by 2\text{ in.} by 1\text{ in.} blocks that can fit in a 3\text{ in.} by 2\text{ in.} by 3\text{ in.} box?

\textbf{(A)}\ 3\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 7

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