geometry(iranian geometry olympiad 2017)

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abrarfiaz
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geometry(iranian geometry olympiad 2017)

Unread post by abrarfiaz » Sun Jan 28, 2018 10:59 pm

4. P1,P2,...,P100 are 100 points on the plane, no three of them are collinear. For each three points, call their triangle clockwise if the increasing order of them is in clockwise order. Can the number of clockwise triangles be exactly 2017?


help me solving the problem

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ahmedittihad
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Re: geometry(iranian geometry olympiad 2017)

Unread post by ahmedittihad » Sun Feb 04, 2018 2:54 am

What help do you need?
Frankly, my dear, I don't give a damn.

abrarfiaz
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Re: geometry(iranian geometry olympiad 2017)

Unread post by abrarfiaz » Mon Feb 05, 2018 7:54 pm

I am being unable of understanding the main concept of the problem. Truly to say ,can't understand the problem. I would be grateful if you do help me

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ahmedittihad
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Re: geometry(iranian geometry olympiad 2017)

Unread post by ahmedittihad » Tue Feb 06, 2018 1:14 pm

Okay so you're having difficulty in understanding what clockwise is. In the picture $ABC$ is clockwise and $A_1B_1C_1$ is counterclockwise.
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Screenshot from 2018-02-06 13-12-01.png
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Frankly, my dear, I don't give a damn.

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samiul_samin
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Re: geometry(iranian geometry olympiad 2017)

Unread post by samiul_samin » Tue Feb 20, 2018 1:57 pm

abrarfiaz wrote:
Mon Feb 05, 2018 7:54 pm
I am being unable of understanding the main concept of the problem. Truly to say ,can't understand the problem. I would be grateful if you do help me
Sketch of the solution
At first there are no such triangle.But if we start roatating the points we will get highest $\dbinom {100}{3}$triangles.And it is obviously greater than $2017$ .So,the number of such triangles can exactly be $2017$.
$\int^{\infty}_0 e^{-x} dx=1$

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