Discussion
In the 4 × 4 array shown below, each cell of the first three rows has either a cross (X) or a number.
| 1 | X | 4 | 3 |
| X | 5 | 5 | 4 |
| 3 | X | 6 | X |
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
Answer: A
The four numbers in the last row add up to 11.
The last row has no crosses, so each of its cells counts its non-cross neighbours in the third row (3, X, 6, X) and beside it in the fourth row.
- First cell: 3 above, X diagonally, its right neighbour: 2.
- Second cell: 3 and 6 diagonally, X above, its two row neighbours: 4.
- Third cell: 6 above, two X's diagonally, its two row neighbours: 3.
- Fourth cell: 6 diagonally, X above, its left neighbour: 2.
So the sum is \(2 + 4 + 3 + 2 = 11\). Answers of 9, 10 or 12 come from counting a cross as a free cell or missing a diagonal neighbour.
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