You are given four unit squares and your task is to form as many rectangles as possible out of it starting from 1 square (by overlapping every squares into each other) to N, one by one (2,3,4...). So you start with 4 unit squares overlapped each other (which will be counted as one rectangle).
But in order to do that, you are allowed to move only 1 square at a time and you need to count one more rectangle than previous turn. That means let's say you have counted 5 rectangles previously, on the next turn, by moving any but one square, you are supposed to find exactly 6 rectangles. If it is not possible, that would be your answer, not necessarily the maximum number of rectangles possible.
At most how many rectangles can you form by moving only one square as you wish?
At most how many rectangles can you form starting from 1 rectangle if you are allowed to move as many squares as possible every turn?
If this question was asked for 2 squares, the answer would be 3 as shown below;