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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?

An empty 4 by 4 grid with column totals 2, 2, 2, 2 on top and row totals 3, 1, 2, 2 on the left

  • A.A 4 by 4 grid with shaded cells (1 = shaded) rows 1011, 0101, 0010, 1100
  • B.A 4 by 4 grid with shaded cells (1 = shaded) rows 1011, 0100, 0011, 1100
  • C.A 4 by 4 grid with shaded cells (1 = shaded) rows 1011, 0110, 0010, 1100
  • D.A 4 by 4 grid with shaded cells (1 = shaded) rows 1011, 0100, 0010, 1101

Answer: B

The correct grid is (ii).

The rows must contain 3, 1, 2 and 2 shaded cells from top to bottom, and every column exactly 2. Reading grid (ii) row by row (1 = shaded): 1011, 0100, 0011, 1100. The row counts are 3, 1, 2, 2 and the column counts are 2, 2, 2, 2, as required.

The others fail somewhere:

  • (i): 1011, 0101, 0010, 1100. The second row has 2 shaded cells and the third only 1.
  • (iii): 1011, 0110, 0010, 1100. The second row has 2, and the third column has 3.
  • (iv): 1011, 0100, 0010, 1101. The third row has 1 and the bottom row 3.

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