Polygon with 50 sides

Probability Level 4

Consider 50 sided strictly convex polygon.

Count number of point of intersection of diagonals which intersect each other inside the polygon.


The answer is 230300.

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Purushottam Abhisheikh by Purushottam Abhisheikh , 24, India

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2 solutions

Aniket Verma
Apr 28, 2015

We know that every quadrilateral has its point of intersection of diagonals lying inside the quadrilateral.

So, in this question the only thing we have to do is to find the number of quadrilateral formed using 50 50 vertices of the given polygon (since each quadrilateral will give one required point of intersection) \text{(since each quadrilateral will give one required point of intersection)}

w h i c h = 50 C 4 = 230300 \color{#D61F06}{which ~=~^{50}C_4~=230300}

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Well done . But how do you ensure that the point of intersection of 2 different pairs of diagonals will never coincide ?

Ujjwal Mani Tripathi - 6 years, 1 month ago
Mas Mus
Jul 23, 2015

Based on this paper , the answer should be 208801 208801

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