If you 99 lines on a piece of paper so that no two lines are parallel to each other and no three lines pass through the same point, how many times will they intersect?. Show all your calculations leading to the answer

50

To find out how many times the 99 lines will intersect, we can use the formula for the maximum number of intersections between n lines. The formula is given by n(n-1)/2.

In this case, we have n = 99. Plugging it into the formula, we get:

99(99-1)/2 = 99(98)/2 = 99 * 49

Now, let's calculate the result:

99 * 49 = 4851

Therefore, the 99 lines will intersect a total of 4851 times.