2003 Pascal Problem 7

In the diagram, the numbers 1, 2, 4, 5, 6, and 8 are substituted, in some order, for the letters A, B, C, D, E, and F, so that the number between and below two numbers is the positive difference between those two numbers. For example, the 7 in the third row is the positive difference between D and 9. Thus D = 2 because 9 - 2 = 7. The value of A + C is

\begin{array}{ccccccc} A & & 10 & & B & & C \\ & D & & 9 & & E & \\ & & 7 & & F & & \\ & & & 3 & & & \end{array}

\textbf{(A)}\ 7\quad \textbf{(B)}\ 12\quad \textbf{(C)}\ 13\quad \textbf{(D)}\ 10\quad \textbf{(E)}\ 14

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Full credit to this problem is given to the CEMC, you may view all Pascal contests here.