The figure in Panel I below is a grid of cells with four rows and four columns. The numbers on the top and on the left represent the number of cells that are to be shaded in that column and row, respectively. Which one of the options shown in Panel II below represents the grid shaded correctly?
To solve the problem, we need to shade the grid in Panel I according to the numbers on the top (columns) and on the left (rows). Each number indicates how many cells are to be shaded in that column or row.
Step-by-step Solution:
- Look at the top numbers for each column in Panel I: 2, 2, 2, 2. This means each column must have exactly 2 shaded cells.
- Look at the left numbers for each row in Panel I: 3, 1, 2, 2. This means the rows must have 3, 1, 2, and 2 shaded cells respectively.
- Now, we analyze each option in Panel II to find which one correctly follows these rules:
- Option (i):
- First Column: 2 cells shaded, correct.
- Second Column: 3 cells shaded, incorrect.
- Third Column: 3 cells shaded, incorrect.
- Fourth Column: 2 cells shaded, correct.
- Option (ii):
- First Column: 2 cells shaded, correct.
- Second Column: 2 cells shaded, correct.
- Third Column: 2 cells shaded, correct.
- Fourth Column: 2 cells shaded, correct.
- Rows:
- First Row: 3 cells shaded, correct.
- Second Row: 1 cell shaded, correct.
- Third Row: 2 cells shaded, correct.
- Fourth Row: 2 cells shaded, correct.
- Option (iii):
- First Column: 3 cells shaded, incorrect.
- Second Column: 3 cells shaded, incorrect.
- Third Column: 1 cell shaded, incorrect.
- Fourth Column: 3 cells shaded, incorrect.
- Option (iv):
- First Column: 2 cells shaded, correct.
- Second Column: 2 cells shaded, correct.
- Third Column: 1 cell shaded, incorrect.
- Fourth Column: 3 cells shaded, incorrect.
- Option (i):
Therefore, the correct option is (ii), as it satisfies both row and column conditions for shading.
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
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
