GATE 2025 CE (CE1) – 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 3 edges meet at each corner. A single piece of wire runs along a path through the corners, and at a corner it passes through along 2 edges, so a corner where 3 edges meet must also have a wire end. Each piece of wire has only 2 ends, so it can serve at most 2 of the 8 corners as an end point. That needs at least $8 \div 2 = 4$ pieces, which means at least 3 cuts. Four pieces can be bent along paths that cover all 12 edges, and soldering joins them at the corners.