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?
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Start with the row that allows only one shaded cell; it eliminates most of the wrong options immediately.
Step 1: Pick the most restrictive clue first.
Look at the row clues 3, 1, 2, 2. The number 1 for row 2 is the strictest clue, since only one cell in the whole second row is allowed to be shaded. Checking row 2 first will eliminate wrong options fastest.
Step 2: Scan row 2 of every option.
In option (i), row 2 has cells shaded in the second and fourth spot, that is 2 shaded cells, already too many. Option (iii) also shades 2 cells in row 2. So (i) and (iii) are out right away.
Option (iv) shades only 1 cell in row 2, and option (ii) also shades only 1 cell in row 2, so both survive this first check.
Step 3: Use the row 3 clue, which should be 2, to separate (ii) and (iv).
In option (ii), row 3 has 2 shaded cells, matching the clue. In option (iv), row 3 has only 1 shaded cell, which breaks the row 3 clue of 2. So option (iv) is eliminated here.
Step 4: Confirm option (ii) fully.
With (i), (iii), and (iv) eliminated, only option (ii) remains. Checking all four rows of (ii) gives 3, 1, 2, 2 and all four columns give 2, 2, 2, 2, both matching Panel I completely.
