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DILR ANSWER KEY & SOLUTION SLOT 1 CAT 2018

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DILR ANSWER KEY & SOLUTION SLOT 1 CAT 2018

PROBLEM 3

Directions for the Q1-Q4: You are given an nxn 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.

Answer the following: Q1. What is the minimum number of different numerals needed to fill a 3x3 square matrix? Q2. What is the minimum number of different numerals needed to fill a 5x5 square matrix? Q3. 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 5x5 matrix? 1. 4 2. 16 3. 9 4. 25 Q4. Suppose that all the cells adjacent to any particular cell must have different numerals. What is the minimum number of different numerals needed to fill a 5x5 square matrix? 1. 25 2. 4 3. 16 4. 9

You are given an nxn 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.

Answer the following: Q1. What is the minimum number of different numerals needed to fill a 3x3 square matrix? Q2. What is the minimum number of different numerals needed to fill a 5x5 square matrix? Q3. 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 5x5 matrix? 1. 4 2. 16 3. 9 4. 25 Q4. Suppose that all the cells adjacent to any particular cell must have different numerals. What is the minimum number of different numerals needed to fill a 5x5 square matrix? 1. 25 2. 4 3. 16 4. 9

You are given an nxn 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.

You are given an nxn 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. 2 4 3

You are given an nxn 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. 2 4 3 4

You are given an nxn 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. 2 4 3 4 2

You are given an nxn 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. 2 2 4 3 4 3 4 2

You are given an nxn 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. 2 3 2 3 2 4 3 4 3 4 4

Answer the following: Q1. What is the minimum number of different numerals needed to fill a 3x3 square matrix? Answer: 4 Q2. What is the minimum number of different numerals needed to fill a 5x5 square matrix? Answer:4 Q3. 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 5x5 matrix? 1. 4 2. 16 3. 9 4. 25 Q4. Suppose that all the cells adjacent to any particular cell must have different numerals. What is the minimum number of different numerals needed to fill a 5x5 square matrix? 1. 25 2. 4 3. 16 4. 9

You are given an nxn 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. 2 3 2 3 2 4 3 4 3 4 4

Answer the following: Q1. What is the minimum number of different numerals needed to fill a 3x3 square matrix? Answer: 4 Q2. What is the minimum number of different numerals needed to fill a 5x5 square matrix? Answer:4 Q3. 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 5x5 matrix? 1. 4 2. 16 3. 9 4. 25 Q4. Suppose that all the cells adjacent to any particular cell must have different numerals. What is the minimum number of different numerals needed to fill a 5x5 square matrix? 1. 25 2. 4 3. 16 4. 9

You are given an nxn 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. 2 3 2 3 2 4 3 4 3 4 4