problem!!!!!!can u solve it??? come if u think u are smart...?

Question

in to how many divisions do "100" lines divide the surface?
in condition that no 3 lines passe one dot.

Answer 1

5051 is the maximum
(n^2 + n + 2)/2 is the generalized answer for n lines.

tevansmd has missed quite a few. A grid of 100 lines, no two of which are parallel and no three of which intersect at the same point will have C(100,2) or 4950 intersection points and can divide the plane into 5051 regions.

Answer 2

Answer: A surface can be divided into 101 to 200 divisions by 100 lines, no three of which pass any point.

Details: 100 parallel lines divide the surface into 101 parts. 100 lines that contain 99 intersections of only two lines per intersection divide the surface into 200 plane segments.

Assumptions: A "surface" is a finite segment of a plane (not curved, has linear boundaries, and contains no holes). The lines are coplanar with the surface, and intersect the surface at more than one point (not tangential to the surface). (If this assumption were false, and the lines were not necessarily coplanar to the surface, then they could intersect the surface at one point, and divide the surface not at all, or "0 to 200 divisions".)

Examples: 100 lines that are coplanar with the surface (assuming the surface is a plane segment) and intersect the surface at least partially must at least divide the surface into 101 plane segments (a segment to the left of every line = 100 segments, plus one to the right of the rightmost line = 101 segments). If every two lines intersects with only themselves in the surface, the surface is divided into 51 (by pairs) + 2*50 (above and below the intersection) = 151 plane segments. 1 line can divide the surface into 2 parts. 2 parallel lines into 3 parts, intersecting into 4 parts. 3 parallel into 4 parts, with one intersection into 5, with two intersections into 6. 4 parallels into 5, intersection into 6, two intersections into 7, three intersections into 8. And so on...

Answer 3

Hi. If the lines are parallel then 102.

BTW, Tylerdurden's bananas!

Answer 4

try this for apples......Te audire no possum. Musa sapientum fixa est in aure.