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What is the minimum number of colours required to fill the spaces in the given diagram without any two adjacent spaces having the same colour?
  • a)
    6
  • b)
    5
  • c)
    4
  • d)
    3
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
What is the minimum number of colours required to fill the spaces in t...
The figure may be labelled as shown.

The spaces P, Q and R have to be shaded by three different colours definitely (since each of these three spaces lies adjacent to the other two).
Now, in order that no two adjacent spaces be shaded by the same colour, the spaces T, U and S must be shaded with the colours of the spaces P, Q and R respectively.
Also the spaces X, V and W must be shaded with the colours of the spaces S, T and U respectively i.e. with the colours of the spaces R, P and Q respectively. Thus, minimum three colours are required.
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Most Upvoted Answer
What is the minimum number of colours required to fill the spaces in t...
The figure may be labelled as shown.

The spaces P, Q and R have to be shaded by three different colours definitely (since each of these three spaces lies adjacent to the other two).
Now, in order that no two adjacent spaces be shaded by the same colour, the spaces T, U and S must be shaded with the colours of the spaces P, Q and R respectively.
Also the spaces X, V and W must be shaded with the colours of the spaces S, T and U respectively i.e. with the colours of the spaces R, P and Q respectively. Thus, minimum three colours are required.
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