Question

The square boxes in the figures given are to be painted with different colours such that no two adjacent boxes (even diagonally) have the same colour. How many minimum colours do you need in each case?

• A. (3, 4)
• B. (4, 4)
• C. (4, 5)
• D. (3, 5)

Hint:

When solving coloring problems in grids, start with corners and move towards the center to minimize the number of colors used.

Answer 1

The Correct Option is A

Step 1: Analyze the configuration of each grid to determine the minimal number of colors needed to ensure no two adjacent squares share a color, including diagonally adjacent.


Step 2: Apply a coloring algorithm, like the four-color theorem for planar graphs, which suggests four colors are sufficient for any planar graph, but fewer may suffice based on configuration.


Step 3: Determine that the first grid can be colored with 3 colors and the second with 4, as it requires at least one additional color due to its configuration.