The minimum number of colours required to paint all the sides of a cube that no two adjacent faces may have the same colours, is
A. 1
B. 2
C. 3
D. 6
Answer: Option C
Solution (By Examveda Team)
The correct answer is C: 3.Here's why:
Imagine a cube in your hand.
You can paint the top face one color (let's say color 1).
Then, you can paint the bottom face the same color (color 1), because it's not adjacent to the top.
Now, all the faces around the sides are adjacent to both the top and bottom.
So, you need a different color (color 2) for one of the side faces.
The face opposite to that side face can also be painted with color 2.
The last two faces will require a third color (color 3) because they are adjacent to both the faces painted with color 1 and color 2.
Therefore, you need a minimum of 3 colors to make sure no two adjacent faces have the same color.
This Question Belongs to Non Verbal Reasoning >> Cubes And Dice
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Related Questions on Cubes and Dice
One face of a cube is adjacent to 4 faces, so we can only colour two opposite faces with the same colour. In a cube, we have three pair of opposite faces.
So for the given conditions, the minimum number of colours required to paint is 3.