[Number Theory]
Problem: If $A, R, M$, and $L$ are positive integers such that $A^{2}+R^{2}=20$ and $M^{2}+L^{2}=10$, compute the product $A \cdot R \cdot M \cdot L$.

Solution: The only positive integers whose squares sum to 20 are 2 and 4 . The only positive integers whose squares sum to 10 are 1 and 3 . Thus $A \cdot R=8$ and $M \cdot L=3$, so $A \cdot R \cdot M \cdot L=\mathbf{2 4}$.

Final answer: 24