GATE CE 2025 Set 1 — Question 4
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General Aptitude → Quantitative Aptitude → 2D & 3D Patterns
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Question
A thin wire is used to construct all the edges of a cube of side by bending, cutting and soldering the wire. If the wire is long, what is the minimum number of cuts required to construct the wire frame to form the cube?
Correct answer
(A) 3
Solution
A cube has 8 vertices, and each vertex has a degree of 3 (3 edges meet at each vertex). In graph theory, a graph can be traversed in a single continuous path (Eulerian path) if it has at most 2 vertices of odd degree. Here, all 8 vertices have odd degrees. To cover all edges with the minimum number of separate paths, we need paths. To obtain 4 separate pieces from a single 12m wire, we need 3 cuts.
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