The question is:
Divide the plane into separate regions using $N$ lines according to the following rules:
- No two lines are parallel.
- No three lines intersect at the same point.
When $N = 1$, the plane is divided into 2 regions. When two lines are drawn in this way, the plane is divided into 4 regions.
I count there are 2 regions for 1 line, 4 regions for 2 lines, 7 regions with 3 lines, 11 regions with 4 lines, 16 regions with 5 lines $\ldots$
I didn’t get a clue for the conjecture. Please give me a hint to get a conjecture?
Best Answer
Conjecture: the number of regions = [(2+n)(n-1)]/2 +2 = (n^2 +n +2)/2