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UKMT Grey Kangaroo, 2018

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

James wrote a different integer from 1 to 9 in each cell of a table. He then calculated the sum of the integers in each of the rows and in each of the columns of the table. Five of his answers were 12, 13, 15, 16 and 17, in some order. What was his sixth answer?

(A) $17$ (B) $16$ (C) $15$ (D) $14$ (E) $13$

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