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 )

Hint:

When solving grid-based problems, carefully examine the neighbors for each cell and apply the given rule systematically. Double-check calculations for edge and corner cells, as their neighbors are fewer.

Answer 1

The Correct Option is A

Step 1: Understand the rule for calculating numbers.

Each cell's value represents the count of its immediate neighbors (left, right, top, bottom, and diagonals) that do not have a cross (X). This rule applies to all cells in the grid.

Step 2: Calculate the numbers for the last row.

We compute the value for each cell in the last row based on the given information:

• Cell (4, 1):
  Neighbors: \( (3,1), (3,2), (4,2) \).
  Non-X neighbors: \( (3,1) = 3 \).
  Value = \( 1 \).
• Cell (4, 2):
  Neighbors: \( (3,1), (3,2), (3,3), (4,1), (4,3) \).
  Non-X neighbors: \( (3,1), (3,3), (4,1) \).
  Value = \( 3 \).
• Cell (4, 3):
  Neighbors: \( (3,2), (3,3), (3,4), (4,2), (4,4) \).
  Non-X neighbors: \( (3,3), (3,4), (4,2) \).
  Value = \( 3 \).
• Cell (4, 4):
  Neighbors: \( (3,3), (3,4), (4,3) \).
  Non-X neighbors: \( (3,3), (3,4) \).
  Value = \( 4 \).

Step 3: Compute the total sum.

The sum of the numbers in the last row is:

\[ 1 + 3 + 3 + 4 = 11. \]

Final Answer: \( \mathbf{(A) \ 11} \)