GATE CSE 2024 | Set 2 | GA Question: 10

Question

In the $4 \times 4$ array shown below, each cell of the first three rows has either a cross $(X)$ or a number.

The number in a cell represents the count of the immediate neighboring cells (left, right, top, bottom, diagonals) NOT having a cross ( $X$ ). Given that the last row has no crosses $(X)$, the sum of the four numbers to be filled in the last row is

• A. $11$
• B. $10$
• C. $12$
• D. $9$

Answer 1

How the last row is calculated? Let's assume that last rows has $x_1,x_2,x_3,x_4$ elements.

1. Neighbour's $(x_1)=3,x_2$, it has 2 neighbour so value= $2$.
2. Neighbour's $(x_2)=3,6,x_1,x_3$, it has $4$ neighbour so value= $4$.
3. Neighbour's $(x_3)=6,x_2,x_4$, it has $3$ neighbour so value= $3$
4. Neighbour's $(x_4)=6,x_3$, it has $2$ neighbour so value= $2$

So value $(x_1+x_2+x_3+x_4)=2+4+3+2=11$

Option $(A)$ is correct.

Answer 2

11

Answer 3

11

The last row will look like this and the sum is 11.

2

4

3

2