# Difference between revisions of "2000 AMC 12 Problems/Problem 12"

## Problem

Let $A, M,$ and $C$ be nonnegative integers such that $A + M + C=12$. What is the maximum value of $A \cdot M \cdot C + A \cdot M + M \cdot C + A \cdot C$?

$\mathrm{(A) \ 62 } \qquad \mathrm{(B) \ 72 } \qquad \mathrm{(C) \ 92 } \qquad \mathrm{(D) \ 102 } \qquad \mathrm{(E) \ 112 }$

## Solution

When $A=M=C=4$ then $AMC+AM+AC+MC = 112$, and that is the greatest answer choice, so the answer is $\boxed{E}$.