Results 1 to 3 of 3

Math Help - Five points on a circle...

  1. #1
    Member
    Joined
    Sep 2006
    Posts
    75

    Five points on a circle...

    Five points on a circle are number 1, 2, 3, 4, and 5 in clockwise order. A bug jumps in a counterclockwise direction from one point to another around the circle. If it is an odd numbered point, it moves two points, and if it on an evn number point, it moves on point. If the bug begins on point 1, what point will it be on after 2007 jumps?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by ceasar_19134 View Post
    Five points on a circle are number 1, 2, 3, 4, and 5 in clockwise order. A bug jumps in a counterclockwise direction from one point to another around the circle. If it is an odd numbered point, it moves two points, and if it on an evn number point, it moves on point. If the bug begins on point 1, what point will it be on after 2007 jumps?
    ok, so i don't recall any "method" to do this problem, so if someone has a method, please post it. i attempted to use common sense (which i don't do often) so let's see what happens.

    if the bug starts at 1, it will jump counter clockwise 2 spaces and end up at 4, since 4 is even, it jumps once to 3, then since 3 is odd, it jumps 2 spaces to one. and then the same process repeats. 1 4 3 1 4 3 1 4 3 1 ....

    the bug takes 3 jumps to complete one cycle, that is, after 3 jumps, it is back on point 1 and start over. now, 2007 is divisible by 3. 2007/3 = 669. so the bug will complete exactly 669 cycles after 2007 jumps, and therefore it will be back to point 1 on it's 2007th jump
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by ceasar_19134 View Post
    Five points on a circle are number 1, 2, 3, 4, and 5 in clockwise order. A bug jumps in a counterclockwise direction from one point to another around the circle. If it is an odd numbered point, it moves two points, and if it on an evn number point, it moves on point. If the bug begins on point 1, what point will it be on after 2007 jumps?
    It starts one 1.
    Notice how it moves.

    1 (initial) --> 4 (1st) --> 3 (2nd) --> 1 (3rd)

    And from here and one it will repeat in this cycle.

    Thus,

    4 (4th) --> 3 (5th) --> 1 (6th)
    4 (7th) --> 3 (8th) --> 1 (9th)
    4 (10th) --> 3 (11th) --> 1 (12th)
    .......
    4 (2005th) --> 3(2006th) --> 1(2007th)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: August 19th 2011, 07:59 AM
  2. help with points on a circle
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: July 5th 2011, 04:07 PM
  3. Points on a circle.
    Posted in the Algebra Forum
    Replies: 8
    Last Post: December 15th 2010, 09:09 AM
  4. Replies: 4
    Last Post: May 2nd 2010, 04:34 PM
  5. Replies: 7
    Last Post: March 15th 2010, 05:10 PM

Search Tags


/mathhelpforum @mathhelpforum