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

Key idea: use the horizontal line AB as the axis of symmetry and pair squares above and below it in the same horizontal positions.

• Step 1: Inspect each vertical column of the figure across AB and count how many unit squares lie above AB and how many lie below AB in that column.

• Step 2: For columns that already have matching squares above and below AB, those are already paired and need no additions.

• Step 3: Identify unpaired squares. In this figure there are three squares above AB without mirrors and three squares below AB without mirrors, so there are six unpaired squares in total.

• Step 4: Add mirror squares for each unpaired square. Adding one mirror square for each of the six unpaired squares creates the required symmetry.

Conclusion: the least number of squares that must be added is 6.

Why other counts fail:

• Adding 4 squares: leaves two squares unpaired, so symmetry is not achieved.

• Adding 5 squares: leaves one square unpaired, so symmetry is not achieved.

• Adding 7 squares: unnecessary, because all missing mirror partners are provided by adding 6 squares; 7 is not minimal.