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?

I'll take it you want number of regions created. This is tedious to count them all, until you realize there's symmetry. Breaking the triangle into 4 equilateral triangles, 3 are just rotations of each other there are 26 in each of these for 78 in those triangles. You can do this  again with the last triangle, giving 14 regions in each of 3 subtriangles. Lastly, you'll note that the remaining triangle has 10 regions.  so you have $3(26+14)+10= 130$ regions. okay slight error possibly in counting in each triangle. still gives you a way to figure it out. 
