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CEMC Gauss (Grade 7), 2003

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer Canada

In the pattern of numbers shown, every row begins with a 1 and ends with a 2. Each of the numbers, not on the end of a row, is the sum of the two numbers located immediately above and to the right, and immediately above and to the left. For example, in the fourth row the 9 is the sum of the 4 and the 5 in the third row. If this pattern continues, the sum of all of the numbers in the thirteenth row is

(A) $12\,270$ (B) $12\,276$ (C) $12\,282$ (D) $12\,288$ (E) $12\,294$

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