GATE CS 2024 Set 2 — Question 10

Let the cells in the last row (Row 4) be denoted as $C_{4,1}, C_{4,2}, C_{4,3}, C_{4,4}$. We are given that the last row has no crosses, so all cells in Row 4 contain numbers. A number in a cell represents the count of neighbors (horizontal, vertical, diagonal) that do not contain 'X'.Grid Context:
Row 3: $3, X, 6, X$
Row 4: $C_{4,1}, C_{4,2}, C_{4,3}, C_{4,4}$ (All are numbers, i.e., not X)Calculating $C_{4,1}$ (Corner):
Neighbors: $(3,1)=3$ (Not X), $(3,2)=X$, $(4,2)$ (Not X).
Count of non-X neighbors = 2.
$C_{4,1} = 2$Calculating $C_{4,2}$ (Edge):
Neighbors: $(4,1)$ (Not X), $(3,1)=3$ (Not X), $(3,2)=X$, $(3,3)=6$ (Not X), $(4,3)$ (Not X).
Count of non-X neighbors = 4.
$C_{4,2} = 4$Calculating $C_{4,3}$ (Edge):
Neighbors: $(4,2)$ (Not X), $(3,2)=X$, $(3,3)=6$ (Not X), $(3,4)=X$, $(4,4)$ (Not X).
Count of non-X neighbors = 3.
$C_{4,3} = 3$Calculating $C_{4,4}$ (Corner):
Neighbors: $(4,3)$ (Not X), $(3,3)=6$ (Not X), $(3,4)=X$.
Count of non-X neighbors = 2.
$C_{4,4} = 2$Sum:
Sum = $2 + 4 + 3 + 2 = 11$.