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More ways to get Braingle...

1000 Point Star

Logic puzzles require you to think. You will have to be logical in your reasoning.

 

Puzzle ID:#32838
Fun:*** (2.17)
Difficulty:**** (3.18)
Category:Logic
Submitted By:lessthanjake789*us*****
Corrected By:cnmne

 

 

 



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

HiImDavidAus*
Sep 04, 2006

Wow, very nice. It looks liek you invested a lot of time into that one!!! Very nice
Punk_RockerAus*
Sep 05, 2006

Someone has wayyy too much free time. xD

Interesting, though...That was cool.
soccerfreak*us*
Sep 05, 2006

how ling did it take u to do this?
jazzmusician46Aau*
Sep 06, 2006

My goodness!
Infrared*us
Sep 18, 2006

Waaaaay too complicated or me.

Great job. Must've been very time-consuming.
googoogjoob
Sep 20, 2006

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.
ulan
Oct 19, 2006

Good puzzle, not so diffucult of one know about phi
Matio_Marious
Oct 29, 2006

Ugh! Math is my best subject, but at the end I'm like "WHAT?!?!?!? Is this English???"
NomadShadow*us*
Nov 08, 2006

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
qwertyopiusa*
Nov 29, 2006

Nice problem!
stil*us*
Dec 02, 2006

Confusing use of "star" and "repeated line segment."
Hope to effect correction.
McBobby1212Aus
Mar 02, 2007

...what?...
sftball_rocks13*
Mar 25, 2007

wow...that was hard
the answer was long. very long. it scared me
good teaser
scary teaser
Odessius
Apr 26, 2007

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
sarggames
Oct 27, 2014

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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