In the 4 x 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
Grid Puzzle Analysis
The problem involves a 4x4 grid where cells contain either a cross ('X') or a number. A number indicates the count of its adjacent neighbors (including diagonals) that are *not* crosses. We are given the first three rows and know the last row contains only numbers. The goal is to find the sum of these numbers in the last row.
Visualizing the 4x4 Grid
The provided string '1X43X5543X6X' represents the first three rows of the grid. Let's visualize it:
| C1 | C2 | C3 | C4 | |
| R1 | 1 | X | 4 | 3 |
| R2 | X | 5 | 5 | 4 |
| R3 | 3 | X | 6 | X |
| R4 | N1 | N2 | N3 | N4 |
Here, N1, N2, N3, and N4 are the unknown numbers in the last row (R4).
Understanding the Neighbor Rule
The core rule is: the number in a cell equals the count of its non-'X' neighbors. Neighbors include cells directly adjacent horizontally, vertically, and diagonally.
Calculating Last Row Numbers
We calculate N1, N2, N3, and N4 by checking their neighbors:
- N1 (Cell R4, C1): Its neighbors are R3C1 (value 3), R3C2 (value X), and R4C2 (value N2). The non-'X' neighbors are R3C1 and R4C2 (since R4 has only numbers). Thus, N1 counts 2 non-'X' neighbors. So, N1 = 2.
- N2 (Cell R4, C2): Its neighbors are R3C1 (3), R3C2 (X), R3C3 (6), R4C1 (N1), and R4C3 (N3). The non-'X' neighbors are R3C1, R3C3, R4C1, and R4C3. Thus, N2 counts 4 non-'X' neighbors. So, N2 = 4.
- N3 (Cell R4, C3): Its neighbors are R3C2 (X), R3C3 (6), R3C4 (X), R4C2 (N2), and R4C4 (N4). The non-'X' neighbors are R3C3, R4C2, and R4C4. Thus, N3 counts 3 non-'X' neighbors. So, N3 = 3.
- N4 (Cell R4, C4): Its neighbors are R3C3 (6), R3C4 (X), and R4C3 (N3). The non-'X' neighbors are R3C3 and R4C3. Thus, N4 counts 2 non-'X' neighbors. So, N4 = 2.
Final Sum Calculation
The values calculated for the last row are N1=2, N2=4, N3=3, and N4=2.
The sum of these four numbers is calculated as:
Sum = N1 + N2 + N3 + N4
Sum = 2 + 4 + 3 + 2
Sum = 11
Important Questions from Puzzles
The diagram below shows a river system consisting of 7 segments, marked P, Q, R, S, T, U, and V. It splits the land into 5 zones, marked Z1, Z2, Z3, Z4, and Z5. We need to connect these zones using the least number of bridges. Out of the following options, which one is correct?
Note: The figure shown is representative.
- A thin wire is used to construct all the edges of a cube of $1 \text{ m}$ side by bending, cutting and soldering the wire. If the wire is $12 \text{ m}$ long, what is the minimum number of cuts required to construct the wire frame to form the cube?
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.
1 1 2 2 X 3 2 X 4 1 2 X 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
In the square grid shown on the left, a person standing at P2 position is required to move to P5 position.
The only movement allowed for a step involves, “two moves along one direction followed by one move in a perpendicular direction”. The permissible directions for movement are shown as dotted arrows in the right.
For example, a person at a given position Y can move only to the positions marked X on the right.
Without occupying any of the shaded squares at the end of each step, the minimum number of steps required to go from P2 to P5 is
- The corners and mid-points of the sides of a triangle are named using the distinct letters P, Q, R, S, T and U, but not necessarily in the same order. Consider the following statements:
• The line joining P and R is parallel to the line joining Q and S.
• P is placed on the side opposite to the corner T.
• S and U cannot be placed on the same side.
Which one of the following statements is correct based on the above information?
