Given that n × n square matrix to be filled with numerals so that no two adjacent cells have the same numeral.

Also, two cells are called adjacent if they touch each other horizontally, vertically or diagonally. As per the given definition, in the following matrix, the following are the cases of adjacent cells.

Question1:

As per the information, we’ve the following diagram for a 3 x 3 matrix to have minimum number of numerals.

So, we require 4 elements to have all different numerals. Ans : 4

Question 2:

As per the information, we’ve the following diagram for a 5 x 5 matrix to have minimum number of numerals.

So, we require 4 elements to have all different numerals. Ans : 4

Question 3:

Even if one mistake is allowed, then also there won’t be any change in the solution given above. Ans : 4

Question 4:

Given that all the cells adjacent to any particular cell must have different numerals, which is satisfied only

when there are at least 9 numerals. Ans : 9