# CAT 2018 Question Paper | CAT LR DI

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

This particular DILR set from 2018 CAT previous year paper is a little unorthodox puzzle owing to the limited numeric data. You are required to get familiarized with eclectic question types so that you do not get surprised with the type of questions. Does it remind you of the Rubix cube? It sure does! Let us see if you are able to solve this question. For many such interesting puzzles, dive into CAT question bank.

## 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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