65,535
It is 10 crossovers.
12
It is 10 crossovers.
depends on the position of the points if points are collinear, we have just only one line, the minimum number. If points are in different position (if any of the two points are not collinear) we have 21 lines (7C2), the maximum number of lines.
22
Six (6)
16
The maximum number of parts a circle can be divided into by using ( n ) straight lines is given by the formula ( \frac{n(n + 1)}{2} + 1 ). For 100 straight lines, this calculation becomes ( \frac{100(100 + 1)}{2} + 1 = 5051 ). Thus, with 100 straight lines, the maximum number of parts a circle can be divided into is 5051.
With n lines, the maximum number is n*(n-1)/2. The minimum is 0.
11
The maximum number of triangles that can be formed by 4 lines depends on how the lines intersect. If no two lines are parallel and no three lines meet at a single point, the maximum number of triangles formed is 4. This occurs because each set of 3 lines can define a unique triangle, and with 4 lines, you can choose 3 out of those 4 in (\binom{4}{3} = 4) ways.
4