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CEMC Gauss (Grade 8), 2001

Number theory Difficulty 2.0 Junior Find the answer Canada

The integers 2, 2, 5, 5, 8, and 9 are written on six cards, as shown. Any number of the six cards is chosen, and the sum of the integers on these cards is determined. Note that the integers 1 and 30 cannot be obtained as sums in this way. How many of the integers from 1 to 31 cannot be obtained as sums?

(A) $4$ (B) $22$ (C) $8$ (D) $10$ (E) $6$

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