2026 AMC 8 Problem 12

In the figure below, each circle will be filled with a digit from 1 to 6. Each digit must appear exactly once. The sum of the digits in neighboring circles is shown in the box between them. What digit must be placed in the top circle?

\textbf{(A)} 2 \qquad \textbf{(B)} 3 \qquad \textbf{(C)} 4 \qquad \textbf{(D)} 5 \qquad \textbf{(E)} it is impossible to fill the circles

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.