In the 4 x 4 array shown below, each cell of the first three rows has either a cross (X) or a number. The number in a ce...

Question

In the 4 x 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:

Row 1: 1  X  4  3
 Row 2: X  5  5  4
 Row 3: 3  X  6  X
 Row 4: ?  ?  ?  ?

A. 11  B. 10  C. 12  D. 9

Accepted Answer

11 Each cell containing a number tells us how many of its at most 8 immediate neighbours (including diagonals) do NOT contain a cross. The last row has no crosses, so each cell in row 4 is simply counted based on how many of its neighbours are non-cross. We need to count non-cross neighbours for each of the four cells in row 4 and sum them.