Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Management
  • You are given an n×n square matrix to be filled with numerals so that no two adjacent cells have the same numeral. Two cells are called adjacent if they touch each

You are given an n×n square matrix to be filled with numerals so that no two adjacent cells have the same numeral. Two cells are called adjacent if they touch each other horizontally, vertically or diagonally. So a cell in one of the four corners has three cells adjacent to it, and a cell in the first or last row or column which is not in the corner has five cells adjacent to it. Any other cell has eight cells adjacent to it.

Question:

What is the minimum number of different numerals needed to fill a 3×3 square matrix? 

 

 

 

 

 

Option: 1

4


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

We are given an n × n square matrix that needs to be populated with numerals in such a way that no two adjacent cells have the same numeral. Here, the term "adjacent" refers to cells that touch each other either horizontally, vertically, or diagonally. In the context of this problem, we need to consider the various cases of adjacent cells within the matrix.

We will begin by assigning the number 1 to the first square that we fill. Our goal is to fill as many squares with the number 1 as possible. Starting from the top-left square, we can fill a total of 4 squares with the number 1.

1    1
     
1   1

Moving on, we can only place the number 2 in 2 out of the 5 remaining squares.

1 2 1
3 4 3
1 2 1

Based on these observations, it is clear that we need a minimum of 4 numbers to fill a 3x3 square matrix while adhering to the condition of no two adjacent cells containing the same number. Therefore, the correct answer is 4.

 

Posted by

avinash.dongre

View full answer

Similar Questions

Latest Question