Results 1 to 4 of 4

Math Help - Game theory of marbles

  1. #1
    Newbie
    Joined
    Oct 2011
    Posts
    2

    Question Game theory of marbles

    In a game, there exist three piles of marbles, each pile with a, b, and c marbles respectively, where a,b,c are natural numbers and a \neq b \neq c. At each turn, you can double the number of marbles in one pile by transporting marbles from one other larger pile (relative to the pile that is going to be doubled, before the doubling). The game is won when any two of the piles have an equal number of marbles.

    Either show that the game can be won from any starting a,b,c, or prove that this is not the case. (In particular, prove that the game cannot be won from every starting a,b,c.)

    A pretty problem, but enlightenment does not come...

    EDIT: Sorry, I recalled the problem from memory, and your post catalyzed my editing of it (your interpretation of what I posted was correct, but I did not remember the problem correctly.)
    Last edited by Neutrino1729; October 6th 2011 at 11:16 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,401
    Thanks
    762

    Re: Game theory of marbles

    the game is not unwinnable for every choice of a,b,c since one scenario is the following:

    a = 1, b = 2, c = 3.

    move 1: move 2 marbles from pile c to pile b. now pile 1 has 1, pile 2 has 4, and pile 3 has 1, game over.

    this suggests that you try to show the game is winnable.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2011
    Posts
    2

    Re: Game theory of marbles

    Thanks for responding, Deveno. However, I realized that my problem statement was incorrect. Thus, your insight is unfortunately nonapplicable (sorry for the error)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,401
    Thanks
    762

    Re: Game theory of marbles

    ah, so you must prove whether or not some intitial combination is unwinnable.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Game theory: Are there any other equilibria in this game?
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: March 7th 2012, 07:45 PM
  2. Game Theory: Hotelling game with 3 players
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: March 26th 2011, 03:08 AM
  3. Game Theory: 2xn game
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: November 17th 2010, 04:53 PM
  4. [game theory] Election game
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: April 22nd 2009, 08:32 AM
  5. can you help me with game theory?
    Posted in the Statistics Forum
    Replies: 0
    Last Post: January 7th 2009, 09:31 AM

Search Tags


/mathhelpforum @mathhelpforum