Q.10 In the 4 × 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
The 4×4 array puzzle from GATE CSE 2024 requires filling the last row, where each number counts immediate non-cross (non-X) neighbors (8 possible directions), given no X’s in that row. The sum of these numbers is 11.
Grid Layout
Row 1: 1 X 4 3 Row 2: X 5 5 4 Row 3: 3 X 6 X Row 4: ? ? ? ?
Numbers indicate verified non-X neighbor counts among existing cells; last row cells (all non-X) count non-X neighbors from rows 1-3.
Last Row Calculation
Each last row cell counts its non-X neighbors above (primarily row 3, plus diagonals).
- Position (4,1): Neighbors include 3 (row 3,col1, non-X), X (row 3,col2). Counts 2 non-X.
- Position (4,2): Neighbors include X (row 3,col2), 6 (row 3,col3, non-X), 5 (row 2,col2, non-X), plus others yielding 4 non-X total.
- Position (4,3): Neighbors include 6 (row 3,col3, non-X), X (row 3,col4), X (row 3,col2). Counts 3 non-X.
- Position (4,4): Neighbors include X (row 3,col4), 6 (row 3,col3, non-X). Counts 2 non-X.
Last row: 2, 4, 3, 2. Sum: 2+4+3+2=11.
Option Analysis
| Option | Sum | Correct? | Reason |
|---|---|---|---|
| (A) 11 | 11 | Yes | Matches 2+4+3+2 from neighbor counts. |
| (B) 10 | 10 | No | Underestimates; ignores full neighbor sets (e.g., position 2). |
| (C) 12 | 12 | No | Overestimates; misreads some X’s as non-X. |
| (D) 9 | 9 | No | Too low; misses diagonal non-X neighbors. |
The 4×4 array cross puzzle from GATE CSE 2024 Set 2 tests logical reasoning skills vital for exams like CSIR NET Life Sciences. Each number counts immediate non-X neighbors (left, right, top, bottom, diagonals—up to 8). With the last row X-free, fill its numbers and sum them: discover why it’s 11.
Key Steps
- Identify the grid: Rows 1-3 fixed with 1, X, 4, 3 / X, 5, 5, 4 / 3, X, 6, X.
- Last row non-X means its cells count row 3’s non-X (3,6) plus upper diagonals.
- Compute: 2 (from 3,X), 4 (from X,6,5+), 3 (from 6,X,X), 2 (from X,6).
Practice Tips
- Verify existing numbers first for consistency.
- List all 8 neighbors per cell systematically.
- Sum confirms option (A) 11 over 10,12,9.
Ideal for CSIR NET quantitative aptitude prep—enhances pattern recognition in biology data analysis.
