Problem Solving

For students of class 6-8 (age 12 to 14)
Fahmida Firoj Ahona
Posts:2
Joined:Mon Dec 28, 2020 9:46 pm
Problem Solving

Unread post by Fahmida Firoj Ahona » Sun Jan 03, 2021 2:00 pm

প্রশ্ন : একটি তলে ৯ টি রেখা আছে। সর্বাধিক কয়টি বিন্দুততে এই রেখাগুলো পরস্পর ছেদ করতে পারবে?

- Please help solving the problem.

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Anindya Biswas
Posts:264
Joined:Fri Oct 02, 2020 8:51 pm
Location:Magura, Bangladesh
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Re: Problem Solving

Unread post by Anindya Biswas » Tue Jan 05, 2021 2:15 pm

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 $=^9C_2=36.$
"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."
John von Neumann

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