Roads Across the City

Square E is the only one that produces continuous lines from the other squares.

Looking at the top 2 squares: The top right square is "made from" by taking away the column on the right of the top-left square. Completing the same operation for the bottom row produces E.

We want all the horizontal and vertical lines to run all the way through the big square. Thus we need two horizontal lines and no vertical line in the square we add. Figure E does the job.

In the top left square there are two lines inside. In the bottom left square there are 3 lines inside. Similarly, in the top right square there is one line inside and hence in the bottom left square there should be 2 line inside. The inside lines are increasing by one, counting from top to bottom.

I realized that the top two boxes have to parts of a line connected and so do the top and bottom left boxes. Thus, I thought that we should complete the other two lines, hence coming up with the answer of E.

square E produces continous lines from other squares

Square E creates lines that reach all the way across the figure, therefore completing the puzzle.

The square on the right-hand side on top is a mirror image of the square beside it to the left, minus the intersecting lines inside the square to the left. Answer E. is a mirror image of the square on bottom left, minus the intersecting lines in that square. Therefore, E. is the counterpart square to the square on bottom left, fitting the pattern.