GATE 2024 AR — Architecture – Question 2

General Aptitude · Spatial Aptitude: Spatial Reasoning and Visualization · 1 mark · Multiple choice

The 15 parts of the given figure are to be painted such that no two adjacent parts with shared boundaries (excluding corners) have the same color. The minimum number of colors required is

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Correct answer: (A) 4

Explanation

The three sectors of the central disk share boundaries pairwise, so they need three different colors. If only those three colors were used, each surrounding region touching two central sectors would be forced to take the third color. Following those forced choices around the disk produces a conflict between adjacent surrounding regions. A fourth color removes that conflict; the remaining outer regions can then be colored using these four colors. Thus the minimum is four, option A.

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