Braingle Lite

1000 Point Star

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 HiImDavid09/04/06
Wow, very nice. It looks liek you invested a lot of time into that one!!! Very nice

Posted by Punk_Rocker09/05/06
Someone has wayyy too much free time. xD Interesting, though...That was cool.

Posted by soccerfreak09/05/06
how ling did it take u to do this? :-?

Posted by jazzmusician4609/06/06
My goodness! :o

Posted by Infrared09/18/06
:o Waaaaay too complicated or me. Great job. Must've been very time-consuming.

Posted by googoogjoob09/20/06
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 ulan10/19/06
Good puzzle, not so diffucult of one know about phi :)

Posted by Matio_Mario10/29/06
Ugh! Math is my best subject, but at the end I'm like "WHAT?!?!?!? Is this English???" :lol: :o

Posted by NomadShadow11/08/06
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 qwertyopiusa11/29/06
Nice problem!

Posted by stil12/02/06
Confusing use of "star" and "repeated line segment." Hope to effect correction.

Posted by McBobby121203/02/07

Posted by sftball_rocks1303/25/07
wow...that was hard :-? the answer was long. very long. it scared me :-? good teaser :D scary teaser :P

Posted by Odessius04/26/07
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 sarggames10/27/14
please help me 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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