Consider the cube shown below with its 8 corners labelled a, b, c, d, e, f, g,
and h. The figure is representative. All corners are to be colored such that any two
corners that are connected by an edge must be of different colors. The minimum
number of colors required to achieve this is ________
Options:
(A) 8
(B) 4
(C) 3
(D) 2
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2026 Q.8)**
**1. Governing Concept**:
- **Topic**: Spatial Aptitude & Cube Symmetries / Vertex Paths
- Navigating vertices of a unit cube along edges and face diagonals.
**2. Option Analysis**:
- Evaluating path lengths and opposite-vertex coordinates confirms Option (B) as the uniquely valid topological statement.
- **Option (B) is CORRECT**.
- **Options (A), (C), and (D) are INCORRECT**: Violate face or edge adjacency rules of a cube.
**3. Final Answer**:
- **Correct Choice**: **B**
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