প্রশ্ন : একটি তলে ৯ টি রেখা আছে। সর্বাধিক কয়টি বিন্দুততে এই রেখাগুলো পরস্পর ছেদ করতে পারবে?
- Please help solving the problem.
Problem Solving
- Anindya Biswas
- Posts:264
- Joined:Fri Oct 02, 2020 8:51 pm
- Location:Magura, Bangladesh
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Re: Problem Solving
Notice that if we consider no wo lines are parallel, and no three are concurrent, then every pair of lines have a unique point of intersection.
In the other direction, every point of intersection corresponds to exactly $2$ lines. So, there is a bijection between the set of all pairs of lines and
the set of intersection points.
So, number of unordered pairs of lines $=^9C_2=36.$
In the other direction, every point of intersection corresponds to exactly $2$ lines. So, there is a bijection between the set of all pairs of lines and
the set of intersection points.
So, number of unordered pairs of lines $=^9C_2=36.$
"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."
— John von Neumann
— John von Neumann