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 determine the correct shading, count the number of shaded cells in each row and column for each option and compare with the constraints from Panel I:

• Row constraints (from top to bottom, Rows 1 to 4): $3, 1, 2, 2$

• Column constraints (from left to right, Columns 1 to 4): $2, 2, 2, 2$

Let us evaluate each panel:

1. Option (i):

   • Row 2 has shaded cells at Column 2 and Column 4 (total $= 2$). This violates the requirement of $1$ shaded cell in Row 2.

2. Option (ii):

   • Row counts:

     • Row 1: Columns 1, 3, 4 $\rightarrow 3$ shaded cells

     • Row 2: Column 2 $\rightarrow 1$ shaded cell

     • Row 3: Columns 3, 4 $\rightarrow 2$ shaded cells

     • Row 4: Columns 1, 2 $\rightarrow 2$ shaded cells

   • Column counts:

     • Column 1: Rows 1, 4 $\rightarrow 2$ shaded cells

     • Column 2: Rows 2, 4 $\rightarrow 2$ shaded cells

     • Column 3: Rows 1, 3 $\rightarrow 2$ shaded cells

     • Column 4: Rows 1, 3 $\rightarrow 2$ shaded cells

   • All row and column constraints are fully satisfied.

3. Option (iii):

   • Row 2 has shaded cells at Column 2 and Column 3 (total $= 2$), violating the Row 2 requirement of $1$.

4. Option (iv):

   • Row 3 has only $1$ shaded cell (at Column 3), violating the Row 3 requirement of $2$.

Thus, only grid (ii) satisfies all the row and column constraints, which corresponds to (B).