Question

In the \(4 \times 4\) array shown below, each cell of the first three rows has either a cross (X) or a number. \[ \begin{array}{|c|c|c|c|} \hline 1 & X & 4 & 3
\hline X & 5 & 5 & 4
\hline 3 & X & 6 & X
\hline ? & ? & ? & ?
\hline \end{array} \] 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:

For such array-based questions, carefully examine the neighboring cells for each cell and count only those that meet the conditions given in the question.

Answer 1

The Correct Option is A

The task is to determine the numbers in the last row such that each represents the count of immediate neighboring cells that do not contain a cross (X). The last row contains no crosses (X), and its neighboring cells are the third row.
For the first cell in the last row (?), the neighbors are: \(3, X\). Only \(3\) is not a cross, so this cell gets \(1\).
For the second cell in the last row (?), the neighbors are: \(3, X, 6\). Both \(3\) and \(6\) are not crosses, so this cell gets \(2\).
For the third cell in the last row (?), the neighbors are: \(X, 6, X\). Only \(6\) is not a cross, so this cell gets \(1\).
For the fourth cell in the last row (?), the neighbors are: \(6, X\). Only \(6\) is not a cross, so this cell gets \(1\).
The numbers in the last row are: \(2, 4, 3, 2\). Their sum is: \[ 2 + 4 + 3 + 2 = 11. \] Final Answer: \[ \boxed{\text{11}} \]