CEMC Pascal, 2003

Number theory Difficulty 3.0 AMC 10/12 Find the answer Canada

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

(A) $7$ (B) $12$ (C) $13$ (D) $10$ (E) $14$

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