(a) If I draw 6 straight lines on a piece of paper, what is the greatest number of regions I can create? (Assume a line always goes from one edge of the paper to another.)

(b) If I draw 4 triangles on a piece of paper, what is the greatest number of regions I can create?

[Note: I'v realised that this question is somewhat ambiguous. The intention was that we were to imagine an "infinite" piece of paper, so that the triangles can't reach the edge of the paper - and this is what the solution is based on.]