CAT 2018 Question Paper | CAT LR DI

CAT Previous Year Paper | CAT DILR | Set 3

This set from CAT 2018 question paper is pretty interesting owing to the minimal data and its heavy dependance of numbers. The grids almost remind us of Rubix Cube and Japanese puzzles! This very question particularly is almost in the lines of Sudoku and turns out like the game itself. Solve this amazing DILR puzzle (and question) from CAT previous year paper and ace your CAT Exam Preparation.

CAT DILR : CAT 2018 Question Paper Slot 1

Set 3 : N x N Square Matrix

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 4 : 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?

  1. 9
  2. 25
  3. 16
  4. 4

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Explanatory Answer

Method of solving this CAT Question on CAT DILR

This is what we get for saying this set is easy!
Let us keep all our 1’s in place and work down from there.
Now, let us take the middle 1 and fill different numerals all around it. We will worry about the rest later on.
CAT DI LR 2018 Slot 1
Hang on, this does not work. The 4 at (2, 4) has four 1’s surrounding it. That cannot be right. Our approach of filling the 1’s is not correct.
Two boxes that have only two cells in between them cannot have the same numeral. If that happens we are in trouble. So, let us restart by keeping this in mind. Fill a few 1’s.
CAT DI LR 2018 Slot 1
Let us fill 1’s that cannot conflict in any way. The way shown in the diagram is good as it ensures that there is no conflict.
CAT DI LR 2018 Slot 1
CAT DI LR 2018 Slot 1
CAT DI LR 2018 Slot 1
CAT DI LR 2018 Slot 1
CAT DI LR 2018 Slot 1
CAT DI LR 2018 Slot 1
So, we can fill the 5 x 5 entirely with 9 different numerals.

The question is "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?"

Hence, the answer is 9

Choice A is the correct answer

 

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