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## 1000 Point Star

 Category: Logic Submitted By: lessthanjake789 Fun: (2.16) Difficulty: (3.18)

Typical "stars" are drawn in connected, but not repeated, line segments. For example, a 5-point star is drawn as such - line segments AC, CE, EB, BD, DA. The segments must always alternate a constant number of points (in the above case, skipping 1 point in between).
Given the information that there is only 1 way to draw a 5-point star, and that there is NO way to draw a 6-point star (in continuous lines, that is), and there are 2 ways to draw a 7-point star, how many different ways are there to draw a 1000-point star?

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Comments on this teaser

 Posted by HiImDavid 09/04/06 Wow, very nice. It looks liek you invested a lot of time into that one!!! Very nice Posted by Punk_Rocker 09/05/06 Someone has wayyy too much free time. xD Interesting, though...That was cool. Posted by soccerfreak 09/05/06 how ling did it take u to do this? :-? Posted by jazzmusician46 09/06/06 My goodness! :o Posted by Infrared 09/18/06 :o Waaaaay too complicated or me. Great job. Must've been very time-consuming. Posted by googoogjoob 09/20/06 Got me on this one! I've been interested in multi-pointed stars ever since a 9-pointed star showed up in a math contest I once entered in middle school. So this one was a lot of fun for me, even though I came up with a wrong answer. Posted by ulan 10/19/06 Good puzzle, not so diffucult of one know about phi :) Posted by Matio_Mario 10/29/06 Ugh! Math is my best subject, but at the end I'm like "WHAT?!?!?!? Is this English???" :lol: :o Posted by NomadShadow 11/08/06 In the course of my job I usually have to do alot of modulus arithmetics, so this took me less than 10 seconds to figure out. Cool one though, this is the first time I think of stars as ranges. Keep up the good work Posted by qwertyopiusa 11/29/06 Nice problem! Posted by stil 12/02/06 Confusing use of "star" and "repeated line segment." Hope to effect correction. Posted by McBobby1212 03/02/07 ...what?... Posted by sftball_rocks13 03/25/07 wow...that was hard :-? the answer was long. very long. it scared me :-? good teaser :D scary teaser :P Posted by Odessius 04/26/07 i dunno, a million? yet i think that defeats the purpose of brain logic. still just grab a pencil and that ones pretty easy. for some people :) Posted by sarggames 10/27/14 please help me out.my answer is 407 or 408. my working all points lie on a circle . there will be n points and gaps between points. let us fix a point from where we start . now for moment we move clockwise . the number of gaps between starting point and first joined point must not be factor of n .if we move around joining points with strategy given the nearest point in the direction opposite to witch we start will have let us say r number of gaps with starting point(in one rotation).let us say number of gaps we are skipping is p.then r is remainder if we divide n by p. from easy visualization we can observe that must not be a factor of p if r is a factor of p then r is factor of n buy euclid rules .n=p(some value let us say q)+r . we want to exclude all p such that r is factor of it .so we must exclude all divisors of n-r where r is factor of n.since in the above case we have to skip no of gaps less than 500 to avoid mirror images .so p have a limit .now using counting of all the number to be excluded .i got my answer which is no close to the given one .there might be a counting mistake but not so much please help

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