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CEMC Gauss (Grade 7), 2004

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer Canada

A grid with 10 rows and some number of columns is made up of unit squares, as shown. A domino ( $\square\square$ ) can be placed horizontally or vertically to exactly cover two unit squares. There are 2004 positions in which the domino could be placed. The number of columns in the grid is

(A) $105$ (B) $106$ (C) $107$ (D) $108$ (E) $109$

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