Results 1 to 4 of 4

Math Help - Circle of numbers

  1. #1
    Junior Member
    Joined
    Jun 2008
    Posts
    44

    Circle of numbers

    The numbers 1, 2 and 3 can be formed in 27 different numbers eg 122, 131,111,331,231. how do you place nine 3:s, nine 2:s and nine 1:s in a circle so when read clockwise each number shows exactly once.

    Think you can motivate your answer?

    By the way is there a better place for this problem in this forum?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    It's easy enough to come up with such sequences by trial and error, for example

    111233121222311333221313232.

    But it looks as though you are asking for more than that, like a systematic method for finding such sequences, or maybe an enumeration of all possible answers. I can't help with that.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2007
    Posts
    33
    This type of sequence is rather well known and is called de Bruijn Sequence. Unfortunately, I don't think there is an easy way of generating such sequences by hand. But for your case, I think the trick is to just avoid repeating the first two numbers that you started with for as long as you can. For example, if you started with
    1231...
    Your first two numbers are 1 and 2, so you should avoid putting 2 next because it would repeat the pattern of 12. Pick either 1 or 3 to make it
    12311... or 12313...
    I can't assure that this always works, but you can test it yourself.

    Edit: This really has nothing to do with number theory, so you might consider putting it in a graph theory forum.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Jun 2008
    Posts
    44

    de Bruijn

    Yeah, I cheched that guy out. I just canīt make anything out of it, at least to this problem.

    I was almost certain that this problem belonged here, but I better replace.

    Thanks!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Numbers on a circle
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: April 26th 2011, 12:35 AM
  2. Lines tangent to a point on a circle in the complex numbers.
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: March 11th 2011, 03:14 PM
  3. Complex Numbers & Unit Circle
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: February 9th 2011, 10:45 PM
  4. Complex Numbers, Unit Circle
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: February 27th 2010, 08:12 PM
  5. Arranging numbers in a circle
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: April 13th 2009, 02:20 AM

Search Tags


/mathhelpforum @mathhelpforum