1000 Point Star
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?
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|
|Posted by stil||12/02/06|
|Confusing use of "star" and "repeated line segment."
Hope to effect correction.|
|Posted by McBobby1212||03/02/07|
|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.
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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