1963 AHSME Problem 37

Given points P_1, P_2,\cdots,P_7 on a straight line, in the order stated (not necessarily evenly spaced). Let P be an arbitrarily selected point on the line and let s be the sum of the undirected lengths PP_1, PP_2, \cdots , PP_7. Then s is smallest if and only if the point P is:

\begin{array}{l} \textbf{(A)}\ \text{midway between }P_1\text{ and }P_7\qquad \\ \textbf{(B)}\ \text{midway between }P_2\text{ and }P_6\qquad \\ \textbf{(C)}\ \text{midway between }P_3\text{ and }P_5\qquad \\ \textbf{(D)}\ \text{at }P_4 \qquad \textbf{(E)}\ \text{at }P_1 \end{array}

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