Question

In the \( 4 \times 4 \) array shown below, each cell of the first three columns has either a cross (X) or a number, as per the given rule. \[ \begin{array}{|c|c|c|c|} \hline 1 & 1 & 2 & \,
\hline 2 & X & 3 & \,
\hline 2 & X & 4 & \,
\hline 1 & 2 & X & \,
\hline \end{array} \] Rule: The number in a cell represents the count of crosses around its immediate neighboring cells (left, right, top, bottom, diagonals). As per this rule, the maximum number of crosses possible in the empty column is:

• A. 0
• B. 1
• C. 2
• D. 3

Hint:

When solving grid-based problems with constraints, check the constraints for each cell carefully and distribute values logically to maximize or minimize conditions as required.

Answer 1

The Correct Option is C

Step 1: Analyze each row to determine the possible placement of crosses in the empty column. Step 2: Evaluate the first row where the number \(2\) in the third column suggests two adjacent crosses. As there is already one cross in the third row, only one more cross can be placed. Step 3: In the second row, the number \(3\) in the third column indicates that it is already satisfied by existing crosses. Hence, no additional crosses can be placed in the empty column. Step 4: In the fourth row, the number \(2\) suggests that two crosses can exist in adjacent cells. Since the previous columns are satisfied, the empty column can accommodate a cross. Conclusion: Based on the above observations, the maximum number of crosses possible in the empty column is 2.