# 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 1 : What is the minimum number of different numerals needed to ﬁll a 3×3 square matrix? [TITA]

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##### Method of solving this CAT Question on CAT DILR

Let us fill out the 4 corner squares with the same numeral

The center cell has to be different from everything else, so let us worry about it right at the end. We can accommodate cells (2,1) and (2,3) with the same number. We can also fill (1, 2) and (3,2) with the same number

The center cell has to be a different number.

Now, this is feasible. Question is, can we fill with only 3 numbers?
Note that the center cell has to be different from everything else.
So, if we had to fill the entire matrix with only 4 numbers, we would have to fill the 8 border squares with only 2 numerals.
This is impossible.

The question is "What is the minimum number of different numerals needed to ﬁll a 3×3 square matrix? [TITA]"

##### Hence, the answer is 4

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