Find how many parts are in a triangle Recently, I got this interesting riddle in a math test, which I still can't solve. Here are the exact words:

Each side of an equilateral triangle was divided into 100 equal parts. Points received
  connected by segments. How many parts did you get?

Here is an example for a triangle with just 3 points on each side:

That much lines really confuses me. I tried to find a ratio between number of lines and parts, and how does each new line drawn divides the others, but it doesn't seem to work. What could be the possible solution to this?

The answer is simple $100^3$. Discard the amount of parts that disappear when three segment get through the same point, At least $99^3$. I assume that you know how to find all other such cases (if exist:))
