GK 2015 Q21
21. 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
Grey Kangaroo 2015, Question 21. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 4
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 ÷ 2 = 4.
Such a solution is possible, for example with wires of length 1 cm, 2 cm, 4 cm and 5 cm, the arrangement of which is left for the reader.
Solution © UK Mathematics Trust, from the GK 2015 solutions.