How many parts do 100 lines divide a plane into when no two are parallel and no three pass through the same point?

Question

I started by trying to find a pattern between the number of lines and parts, but it seems to be pretty random. (I may have split the plane incorrectly). Can someone give me a hint to if there is a pattern or a clear method?

Answer 1

Hint: think of the problem as a planar graph in which the intersections of lines are vertices and the line segments are edges. In order to actually get a graph you can add a huge circle outside the graph so that the lines don't go to infinity).

Then apply euler's formula. The number of segments and vertices is easy to calculate inductively.