if u draw 80 lines on a piece of paper so no 2 lines r parallel......how many intercection points will there b

Question

also becides no 2 lines being parallel no 3 lines can pass though the same point.

Answer 1

Two non-parallel lines will cross at one point, that may not be on your sheet of paper since lines have infinite length. There is no way to solve this. You could draw 80 almost parallel lines that never crossed on a sheet of paper or you could draw 79 almost parallel horizontal lines then one vertical line and end up with 79 intersections.

Answer 2

If no two lines are parallel and no three lines pass thru the same point, then they will each intersect with the other 79 lines. Since you are double counting, divide by two.

Number of intersection points is: 80*79/2 = 3160

Answer 3

What's the maximum number (assuming they all intersect)?

Gold rule of maths - is there a pattern?

First line, no intersection points;
Second line, one point;
Third line, two more points, (so 3 in total so far);
Fourth line must cross the existing three (because not allowed to repeat intersections), so it adds 3 points (so 6 in total so far)...

Spot the pattern?

What's the total number? (Hint: Gauss solved the sum of this pattern when he was at school).