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The least number of squares to be added in the figure to make AB a line of symmetry is

Unit squares drawn along a horizontal dashed line AB: one square above the line and five squares below it in two groups

  • A.6
  • B.4
  • C.5
  • D.7

Answer: A

At least 6 squares must be added.

Look carefully at the drawing. Above the line AB there is one square. Below the line there are five: in the left group a square to the left of the vertical column and a square at the bottom of that column; in the right group two squares side by side with one more below the right-hand one. The cell directly below the upper square is not a square: it has no right-hand side, so it is only the gap between drawn squares.

For AB to be a line of symmetry, every square must have a mirror image on the other side. Each of the five squares below needs a partner above (5 squares), and the square above needs a partner directly below it, which is missing (1 square). That makes 6.

5 is the answer you get if you read the open cell below the upper square as a square; 4 and 7 do not match any count of the figure.

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