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UKMT Senior Mathematical Challenge, 2016

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Points are drawn on the sides of a square, dividing each side into $n$ equal parts (so, in the example shown, $n = 4$ ). The points are joined in the manner indicated, to form several small squares (24 in the example, shown shaded) and some triangles. How many small squares are formed when $n = 7$ ?

(A) $56$ (B) $84$ (C) $140$ (D) $840$ (E) $5040$

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