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UKMT Grey Kangaroo, 2015

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

Andrew has seven pieces of wire of lengths $1$ cm, $2$ cm, $3$ cm, $4$ cm, $5$ cm, $6$ cm and $7$ cm. He bends some of the pieces to form a wire frame in the shape of a cube with edges of length $1$ cm without any overlaps. What is the smallest number of these pieces that he can use?

(A) $1$ (B) $2$ (C) $3$ (D) $4$ (E) $5$

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