# CAT 2018 Question Paper | CAT LR DI

###### CAT Previous Year Paper | CAT DILR | Set 3

CAT DI LR section has become increasingly tough beginning from 2015. DILR used to have distinct Data Interpretation sets and Logical reasoning puzzles. It used to be about computation and ability to read charts, graphs and tables for the Data Interpretation and Logical reasoning used to have Family tree, grid puzzles, arrangement, tournaments, cubes as some standard forms of puzzles.Since 2015 this pattern has been broken. With passing years, even the distinction between DI and LR has come down significantly. All you get in that one hour, are 8 high quality puzzles, with more than a few of them being significantly tough. Between CAT 2017 Question paper and CAT 2018 Question paper, you get to solve 32 actual CAT puzzles. This page intends to provide you just that. So, head on and crack those puzzles!

## 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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##### 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.

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.

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.

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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