12. Laura wishes to cut this shape, which is made up of nine small squares, into pieces that she can then rearrange to make a $3 \times 3$ square.
What is the smallest number of pieces that she needs to cut the shape into so that she can do this?

A 2
B 3
C 4
D 5
E 6
Solution: B
In a $3 \times 3$ square each row and column contains just 3 squares. So none of the pieces that Laura uses to make the square can be more than 3 squares long. It follows that the squares labelled $a$ and $b$ must be in different pieces, as also must be the squares labelled $b$ and $c$. So there must be at least three pieces. The diagrams below show how Laura can fulfill her task using 3 pieces.