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Discussion of Problem 1591. Abstract Thinking

Too simple Ac,may be checker wrong
Posted by svr 31 Oct 2007 11:08
Let S4(n),S5(n),S6(n)- number of different
4-poligons,5-poligons and 6-poligons in n poligon.
I have AC using formula F(n)=4*S4(n)+5*S5(n)+S6(n).
But this formula can not be right because
in different 6-poligons 3 hords may intersect in
the same point and this triangle will be counted
more the once.
Re: Too simple Ac,may be checker wrong
Posted by RLE 1 Nov 2007 18:54
Your worry is superfluous
This condition (put mentally n points on its periphery at equal distances) can guarantee that there will not be different 6-poligons 3 hords may intersect in
the same point and this triangle will be counted
more the once

P.S My English is so poor...
Re: Too simple Ac,may be checker wrong
Posted by svr 1 Nov 2007 22:02
My suspictions based on considering
ideal 12-poligon in which exist two ideal
6- sub-poligons which different and distinvished
by rotation and having common centre in
which their hord intersected.


Edited by author 01.11.2007 22:26
Re: Too simple Ac,may be checker wrong
Posted by Denis Koshman 20 Jul 2008 17:11
I doubt anyone can mentally put 2000 points on a circle =)
Re: Too simple Ac,may be checker wrong
Posted by Alexander Georgiev 2 Oct 2008 05:56
Hah, I on the other hand believe everyone can mentally (and not only) put infinitely many points on a circle. After all - isn't that the definition of a circle? (Infinitely many points with equal distance from one other point - the center?) :D
Re: Too simple Ac,may be checker wrong
Posted by Programmer 9 Jan 2010 04:08
F(n)=4*S4(n)+5*S5(n)+S6(n)
Why is it true and how to guess about it?
ADMIN(s) help
Posted by mirzauzairbaig 13 Jan 2010 23:40
a picture is needed to understand ! please assist
Re: Too simple Ac,may be checker wrong
Posted by 2rf [Perm School #9] 14 Aug 2010 20:46
Yes, I was thinking about it too and I understand it now. In fact, it's said in statement that interesting triangle is not a triangle but "any three different chords from this set that intersect pairwise" and "at least one of their intersection points lies inside the circle". Therefore, three segments intersecting in one point are interesting triangle( and not a triangle).

It's like saying that interesting triangle is a four-sided figure =)