2025 Cayley Problem 9

Teddy has 10 rectangular blocks each of which measures 3 cm by 4 cm by 5 cm. He builds a stack that is exactly 21 cm high, where each block can be stacked on any of its faces. What is the smallest number of blocks that Teddy could use to make this stack?

\textbf{(A)}\ 4\quad \textbf{(B)}\ 5\quad \textbf{(C)}\ 6\quad \textbf{(D)}\ 7\quad \textbf{(E)}\ 8

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.