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?
Show Hint
Count the shaded cells in each row and each column of every option and compare with Panel I's numbers.
Step 1: Note what each number means.
Panel I is a 4 row by 4 column grid. Each number on top tells how many cells in that column must be shaded, and each number on the left tells how many cells in that row must be shaded. The column targets are all 2, and the row targets from top to bottom are 3, 1, 2, 2. A correct answer must match both sets of numbers at the same time.
Step 2: Count the shaded cells in each row of option (ii).
Reading option (ii) row by row: row 1 has 3 shaded cells (columns 1, 3, 4), row 2 has 1 shaded cell (column 2), row 3 has 2 shaded cells (columns 3, 4), and row 4 has 2 shaded cells (columns 1, 2). These row counts are 3, 1, 2, 2, which line up exactly with the row targets 3, 1, 2, 2.
Step 3: Check the columns of option (ii) too.
Column 1 is shaded in rows 1 and 4, giving 2. Column 2 is shaded in rows 2 and 4, giving 2. Column 3 is shaded in rows 1 and 3, giving 2. Column 4 is shaded in rows 1 and 3, giving 2. Every column comes out to 2, matching the column targets.
Step 4: Rule out the rest.
Checking rows the same way in options (i), (iii), and (iv) turns up at least one row where the shaded count does not equal the needed row target, even where the columns still add up to 2, so those three panels get rejected.
Final Answer:
Only option (ii) satisfies every row sum and every column sum at once.
\[ \boxed{\text{Option B, panel (ii)}} \]
