Question: How many blocks can 999 lines divide a plane into?
My understanding is that 999 lines can theoretically intersect 999 lines to maximize the cut.
Have a zero line
One plane: 1
There are 1 line
The original plane is retained and a new plane is added, that is, 1+1
Two lines intersect
The original plane is retained, and two new planes are added, namely, 1+1+2
Three lines intersect
The original plane is retained, and three new planes are added, namely, 1+1+2+3
Four lines intersect
The original plane is retained and four new planes are added, namely, 1+1+2+3+4
There are 999 intersecting lines
That is: 1 + 1 + 2 + 3 + 4 +… +998+999 = 1+(1+999)*999/2 = 499501