CAT 2018 Slot 1 — DILR Question 20
Answer the following question based on the information given below.
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.
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 5×5 square matrix?
Answer & solution
Correct answer: 9
- A
25
- B
16
9
- D
4
Assuming that the particular cell is not a cell at one of the corner, it has 8 adjacent cells.
Hence, 8 + 1 = 9 different numerals are required to fill the particular cell and the adjacent cells.
Earlier we have seen that 4 different numerals are required to fill a 5 × 5 matrix. Hence, 9 different numerals will be definitely sufficient to fill the 5 × 5 matrix.
Hence, option (c).
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