Results 1 to 4 of 4
Like Tree1Thanks
  • 1 Post By SlipEternal

Thread: Combinatorics problem

  1. #1
    Member Vinod's Avatar
    Joined
    Sep 2011
    From
    Mumbai (Bombay),India
    Posts
    195
    Thanks
    3

    Lightbulb Combinatorics problem

    In how many ways can two rooks of different colours be put on a chessboard so that they can take each other?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,024
    Thanks
    2763

    Re: Combinatorics problem

    So that they can or so that they cannot?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member Vinod's Avatar
    Joined
    Sep 2011
    From
    Mumbai (Bombay),India
    Posts
    195
    Thanks
    3

    Re: Combinatorics problem

    They can take each other
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2010
    Posts
    2,381
    Thanks
    902

    Re: Combinatorics problem

    Put one rook on the board. There are 64 ways of doing that. regardless of where the rook is on the board, there are seven squares in the same rank and seven squares in the same file where the second rook can be such that the two rooks are attacking each other. That is $64\cdot 14$ different ways (since the two rooks are of different colors). If they are the same color, divide by 2.
    Thanks from Vinod
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Combinatorics problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Feb 17th 2015, 09:08 AM
  2. Combinatorics Problem
    Posted in the Statistics Forum
    Replies: 8
    Last Post: Jul 14th 2012, 05:15 AM
  3. problem in combinatorics
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Oct 21st 2011, 08:23 AM
  4. Combinatorics problem
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Apr 20th 2010, 01:25 PM
  5. Combinatorics Problem
    Posted in the Discrete Math Forum
    Replies: 9
    Last Post: Mar 5th 2008, 08:29 AM

Search Tags


/mathhelpforum @mathhelpforum