Yukihira is counting the minimum number of lines $m$, that can be drawn on the plane so that they intersect in exactly $200$ distinct points.What is $m$?
Problem
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Tags: combinatorics
adhikariprajitraj
10.03.2018 14:57
For $m$ no. of lines the maximum possible no. of intersections is given by $\frac{(m)(m-1)}{2}$. So we have, $$m^2-m-400=0$$Solve the equation you get around $20.5$, then you take, $$\lceil 20.5 \rceil=21$$So, 21 minimum lines has to be drawn for the intersection at exactly 200 points!
Helium
10.03.2018 16:04
what do you mean by $\frac{(m)(m-1)}{2}$?
adhikariprajitraj
10.03.2018 16:05
Helium wrote: what do you mean by $\frac{(m)(m-1)}{2}$? It is the greatest no. of intersection of m lines!
Helium
10.03.2018 16:09
oh! sorry to bother you!