GATE 2025 CH – Question 4
A thin wire is used to construct all the edges of a cube of 1 m side by bending, cutting and soldering the wire. If the wire is 12 m long, what is the minimum number of cuts required to construct the wire frame to form the cube?
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Correct answer: (A) 3
Explanation
A cube has 8 corners and at each corner 3 edges meet, an odd number. A continuous wire can pass through a corner using 2 edges, but a corner with an odd number of edges must be the start or end of a piece of wire. All 8 corners are odd, and every piece of wire has only 2 ends, so at least $8 / 2 = 4$ pieces are needed. Cutting the wire into 4 pieces takes 3 cuts. This can be done, for example, with four paths that together cover the 12 edges.