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1000 Point Star

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


Puzzle ID:#32838
Fun:*** (2.16)
Difficulty:**** (3.18)
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?


It's not guess work. Think of factors and mirror images. Try drawing out examples.

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Sep 04, 2006

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

Someone has wayyy too much free time. xD

Interesting, though...That was cool.
Sep 05, 2006

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

My goodness!
Sep 18, 2006

Waaaaay too complicated or me.

Great job. Must've been very time-consuming.
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.
Oct 19, 2006

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

Ugh! Math is my best subject, but at the end I'm like "WHAT?!?!?!? Is this English???"
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
Nov 29, 2006

Nice problem!
Dec 02, 2006

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

Mar 25, 2007

wow...that was hard
the answer was long. very long. it scared me
good teaser
scary teaser
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
Oct 27, 2014

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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