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Category: | Logic |

Submitted By: | lessthanjake789 |

Fun: | (2.17) |

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?

Show Hint | Show Answer |

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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