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There are 36 unique quadrilaterals in a 3x3 square grid:

14 squares = 9 (1x1) 4 (2x2) 1 (3x3)

22 rectangles = 6 (1x2) 6 (2x1) 6 (3x3) 2 (2x3) 2 (3x2)

(the total number of quadrilaterals formed by 3 x 3 pin sets will be larger, i.e. 78)

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