Fall 2021 AMC 10 B

Answer (E): When the four numbers are added, the digits $1$, $2$, $3$, and $4$ appear exactly once in each column of the addition problem, as shown in the figure. \begin{array}{@{}r@{}l} & 1234 \\ & 2341 \\ & 3412 \\ + & 4123 \\ \hline \end{array} The digits sum to $10$, producing a carry of $1$ in each column. The sum of the four numbers is therefore $11,110$.