Question:

Let $x,y,z$ be three natural numbers such that $x+y+z=10$. The maximum possible value of $xyz+xy+yz+zx$ is

Step-by-Step Solution

Key Concept: By AM-GM: $(x+1)(y+1)(z+1)$ is maximized when $x+1,y+1,z+1$ are as equal as possible. $(x+1)(y+1)(z+1)=xyz+xy+yz+zx+x+y+z+1$.

$(x,y,z)=(3,3,4)$: max $=69$.

Correct Answer: 3