If all the faces of a rectangular box (cuboid) with dimensions 4 times 3 times 2 cm are to be painted, what is the minimum number of distinct colours needed so that no two adjacent faces (sharing an edge) have the same colour?

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EEJ MAIN Aptitude QUESTION #10957

Question 1

If all the faces of a rectangular box (cuboid) with dimensions \(4 \times 3 \times 2\ cm are to be painted, what is the minimum number of distinct colours needed so that no two adjacent faces (sharing an edge) have the same colour?

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Correct Answer Explanation

A cuboid has 3 pairs of opposite faces: (top-bottom), (front-back), (left-right).

Each pair of opposite faces are NOT adjacent to each other. All other combinations of faces (from different pairs) ARE adjacent.

We need to colour 3 pairs such that any two faces from different pairs have different colours.

This is equivalent to colouring 3 objects (pairs) where each pair must differ from the other two = needs 3 colours (one colour per pair of opposite faces).

Minimum = 3 colours: colour 1 for top/bottom, colour 2 for front/back, colour 3 for left/right.

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