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Number theory Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Molly has a set of cards numbered $1$ to $12$ . She places eight of them at the vertices of an octagon so that the sum of every pair of numbers at opposite ends of an edge of the octagon is a multiple of $3$ . Which numbers did Molly not place?

(A) $1, 5, 9$ and $12$ (B) $3, 5, 7$ and $9$ (C) $1, 2, 11$ and $12$ (D) $5, 6, 7$ and $8$ (E) $3, 6, 9$ and $12$

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