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GATE 2026 XH2 (English) – Question 8

General Aptitude · Analytical Aptitude: Logical Reasoning and Deduction · 2 marks · Multiple choice

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 ________

A cube drawn with its eight corners labelled a to h.
  1. 8
  2. 4
  3. 3
  4. 2

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Show answer and explanation

Correct answer: (D) 2

Explanation

At least two colours are needed because any edge joins two corners that must differ. Two are enough: colour corners so that the two ends of every edge get different colours. On a cube, moving along an edge changes exactly one of the three coordinates, so colouring a corner by whether the number of its coordinates equal to 1 is even or odd gives different colours at both ends of every edge. So the minimum is 2.