2005 AMC 12A Problem 11

How many three-digit numbers satisfy the property that the middle digit is the average of the first and the last digits?

\textbf{(A) } 41 \qquad \textbf{(B) } 42 \qquad \textbf{(C) } 43 \qquad \textbf{(D) } 44 \qquad \textbf{(E) } 45

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