21. Andrew has seven pieces of wire of lengths $1 \mathrm{~cm}, 2 \mathrm{~cm}, 3 \mathrm{~cm}, 4 \mathrm{~cm}$, $5 \mathrm{~cm}, 6 \mathrm{~cm}$ and $7 \mathrm{~cm}$. He bends some of the pieces to form a wire frame in the shape of a cube with edges of length $1 \mathrm{~cm}$ without any overlaps. What is the smallest number of these pieces that he can use?
A 1
В 2
C 3
D 4
E 5
21. D Since there is no overlap of wires, each vertex of the cube requires at least one end of a piece of wire to form it. A cube has eight vertices and each piece of wire has two ends, so the minimum number of pieces of wire required is $8 \div 2=4$.
Such a solution is possible, for example with wires of length $1 \mathrm{~cm}, 2 \mathrm{~cm}, 4 \mathrm{~cm}$ and $5 \mathrm{~cm}$, the arrangement of which is left for the reader.