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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.
Q. Suppose you are allowed to make one mistake, that is, one pair of adjacent cells can have the same numeral. What is the minimum number of different numerals required to fill a 5×5 matrix?
- a)25
- b)4
- c)16
- d)9
Correct answer is option 'D'. Can you explain this answer?
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You are given an n×n square matrix to be filled with numerals so that...
It has been given that all the cells adjacent to a cell must have different numerals. Let us start filling the matrix from the central square since the central square has the maximum number of squares adjacent to it (8) and it will be easier to work around the central 9 squares.
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A minimum of 9 numbers will be required to fill the central 9 squares.
Now we have to fill the remaining squares. Let us start with the top left square. We have to check whether the 9 numbers will be sufficient to fill all the squares such that no 2 squares adjacent to a square have the same number. We can use any of the 3 numbers 4, 5, and 6 to fill the top left square since none of the numbers in the second column are adjacent to these numbers.
Let us assume that we use 4 to fill the top left square. Now, one of the cells with the number 4 has become adjacent to the cell with number 2 and no other cell adjacent to cell with number 2 (in the second row and second column) can have 4 as its neighbour. Similarly, we can fill the first row with numbers 8 and 7.
In essence, we are trying to create a gird around each of the numbers in the corners of the inner 3x3 matrix such that no 2 cells adjacent to a cell have the same number. Filling the other cells similarly, we get the following matrix as one of the possible cases.
We need a minimum of 9 numbers to fill a 5x5 matrix such that for any cell, no 2 cells adjacent to it contain the same value. Therefore, option D is the right answer.
Most Upvoted Answer
You are given an n×n square matrix to be filled with numerals so that...
Minimum Number of Different Numerals Required for 5x5 Matrix
Approach:
- To minimize the number of different numerals required in the matrix, we need to strategically place the numerals in a way that minimizes the chances of having adjacent cells with the same numeral.
- We can start by filling the diagonals with the same numeral as they do not share any adjacent cells.
Diagonal Cells:
- We can start by filling the diagonal cells with different numerals. This will ensure that no two adjacent cells in the diagonal have the same numeral.
Adjacent Cells:
- Next, we can fill the cells adjacent to the diagonal cells with a different numeral than the one in the diagonal. This will ensure that no two adjacent cells have the same numeral.
Repeating the Pattern:
- By repeating this pattern, we can fill the entire 5x5 matrix with only 9 different numerals while allowing one pair of adjacent cells to have the same numeral.
Therefore, the minimum number of different numerals required to fill a 5x5 matrix while allowing one mistake is 9 (option D).
Approach:
- To minimize the number of different numerals required in the matrix, we need to strategically place the numerals in a way that minimizes the chances of having adjacent cells with the same numeral.
- We can start by filling the diagonals with the same numeral as they do not share any adjacent cells.
Diagonal Cells:
- We can start by filling the diagonal cells with different numerals. This will ensure that no two adjacent cells in the diagonal have the same numeral.
Adjacent Cells:
- Next, we can fill the cells adjacent to the diagonal cells with a different numeral than the one in the diagonal. This will ensure that no two adjacent cells have the same numeral.
Repeating the Pattern:
- By repeating this pattern, we can fill the entire 5x5 matrix with only 9 different numerals while allowing one pair of adjacent cells to have the same numeral.
Therefore, the minimum number of different numerals required to fill a 5x5 matrix while allowing one mistake is 9 (option D).
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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.Q. Suppose you are allowed to make one mistake, that is, one pair of adjacent cells can have the same numeral. What is the minimum number of different numerals required to fill a 5×5 matrix?a) 25b) 4c) 16d) 9Correct answer is option 'D'. Can you explain this answer?
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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.Q. Suppose you are allowed to make one mistake, that is, one pair of adjacent cells can have the same numeral. What is the minimum number of different numerals required to fill a 5×5 matrix?a) 25b) 4c) 16d) 9Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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.Q. Suppose you are allowed to make one mistake, that is, one pair of adjacent cells can have the same numeral. What is the minimum number of different numerals required to fill a 5×5 matrix?a) 25b) 4c) 16d) 9Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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.Q. Suppose you are allowed to make one mistake, that is, one pair of adjacent cells can have the same numeral. What is the minimum number of different numerals required to fill a 5×5 matrix?a) 25b) 4c) 16d) 9Correct answer is option 'D'. Can you explain this answer?.
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.Q. Suppose you are allowed to make one mistake, that is, one pair of adjacent cells can have the same numeral. What is the minimum number of different numerals required to fill a 5×5 matrix?a) 25b) 4c) 16d) 9Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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.Q. Suppose you are allowed to make one mistake, that is, one pair of adjacent cells can have the same numeral. What is the minimum number of different numerals required to fill a 5×5 matrix?a) 25b) 4c) 16d) 9Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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.Q. Suppose you are allowed to make one mistake, that is, one pair of adjacent cells can have the same numeral. What is the minimum number of different numerals required to fill a 5×5 matrix?a) 25b) 4c) 16d) 9Correct answer is option 'D'. Can you explain this answer?.
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