# CAT 2018 Question Paper | CAT LR DI

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

This is a beautiful set with many layers as that of a Rubix cube. This question test your optimization skills and how well you are able to cope up with the minimization and maximization. Essentially, the questions in the DILR section CAT question paper deals with the basics rather than complex algorithms. Try your hands on this wonderful problem from 2018 CAT previous year paper and look how well can solve logic-based questions in your CAT preparation online.

## 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 2 : What is the minimum number of different numerals needed to ﬁll a 5×5 square matrix? [TITA]

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

Now, we have worked with a 3 x 3. We know that the 4 corner squares of the 3 x 3 can be the same number.
So, let us fill out a set of 3 x 3’s within this 5 x 5. We can build from there.

Now, let us fill out squares in between the 1’s row wise and then column wise.

Now, let us fill out squares in between the 1’s row wise and then column wise.
Now, this wonderful matrix fills itself. All the missing numbers should be the 4th numeral.
We know that to fill a mere 3 x 3 we needed at least 4 numerals.
If we have filled a 5 x 5 with 4 numerals, this fills me with enormous confidence.
Now, we can kill this set.

The question is "What is the minimum number of different numerals needed to ﬁll a 5×5 square matrix? [TITA]"

##### Hence, the answer is 4

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