Question 10

Let the columns of unit squares from left to right be indexed $c \in \{1, 2, 4, 5\}$ (with an empty gap at column $3$), and let rows above line $\text{AB}$ be $+1, +2$ and rows below line $\text{AB}$ be $-1, -2$.

Inspecting the figure, the $6$ existing unit squares are located at:

1. $(2, +1)$ (above $\text{AB}$, left group) - notice that $(2, -1)$ directly below it has no right vertical edge and is an empty space, not a square.
2. $(1, -1)$ (below $\text{AB}$, left group)
3. $(2, -2)$ (two rows below $\text{AB}$, left group)
4. $(4, -1)$ (below $\text{AB}$, right group)
5. $(5, -1)$ (below $\text{AB}$, right group)
6. $(5, -2)$ (two rows below $\text{AB}$, right group)

None of these $6$ squares has its reflection $(c, -r)$ across $\text{AB}$ present in the figure. Therefore, we must add the $6$ reflected squares at $(2, -1), (1, +1), (2, +2), (4, +1), (5, +1),$ and $(5, +2)$, so the minimum number of squares to be added is $6$.