Results 1 to 6 of 6

Math Help - Chessboard Problem!

  1. #1
    Member
    Joined
    May 2006
    Posts
    148
    Thanks
    1

    Chessboard Problem!

    Suppose a queen starts out standing on the third square on a chessboard at the very top. That is, the queen stands on the 3rd sqaure from the left. Two players play a game where each player takes a turn moving the queen:

    a.) either horizontally to the right
    b.) or vertically downward
    c.) or diagonally in south-east direction

    For the above, they can move the queen as many squares as they want.

    The first player that can place the queen on the lower-left most right square of the chessboard wins the game.

    Who will win, and what is the winning strategy for each n and m?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    May 2006
    Posts
    148
    Thanks
    1
    Any suggestions on where to even start or how to approach this question? How do you suggest trying to come up with an equation that works in general? Different cases?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member Glaysher's Avatar
    Joined
    Aug 2006
    From
    Newton-le-Willows
    Posts
    224
    Quote Originally Posted by fifthrapiers View Post
    Suppose a queen starts out standing on the third square on a chessboard at the very top. That is, the queen stands on the 3rd sqaure from the left. Two players play a game where each player takes a turn moving the queen:

    a.) either horizontally to the right
    b.) or vertically downward
    c.) or diagonally in south-east direction

    For the above, they can move the queen as many squares as they want.

    The first player that can place the queen on the lower-left most right square of the chessboard wins the game.

    Who will win, and what is the winning strategy for each n and m?
    Lower left most right square?

    What n and m? Do youmean an n by m board rather than the standard board.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    May 2006
    Posts
    148
    Thanks
    1
    "The first player that can place the queen on the lower-left most right square of the chessboard wins the game.

    Who will win, and what is the winning strategy for each n and m?"

    Err, sorry. I meant the first player that can place the queen on the lower-right most square (IE: bottom right corner) of the chessboard wins.

    "What n and m? Do youmean an n by m board rather than the standard board."

    Yes.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    May 2006
    Posts
    148
    Thanks
    1
    "What n and m? Do youmean an n by m board rather than the standard board."

    Nevermind on that. I misread the question. It's just "what is the winning strategy." No n's or m's.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member
    Joined
    Apr 2006
    Posts
    399
    Awards
    1
    Quote Originally Posted by fifthrapiers View Post
    Suppose a queen starts out standing on the third square on a chessboard at the very top. That is, the queen stands on the 3rd sqaure from the left. Two players play a game where each player takes a turn moving the queen:

    a.) either horizontally to the right
    b.) or vertically downward
    c.) or diagonally in south-east direction

    For the above, they can move the queen as many squares as they want.

    The first player that can place the queen on the lower-left most right square of the chessboard wins the game.

    Who will win, and what is the winning strategy for each n and m?
    Similarly to analyzing the game in this thread, analyze the game backwards from last move.

    Form the board, which is effectively 8x6 because the queen cannot move to the left. See below. Starting from the lower right corner, mark a position as W for winning if a player can win outright from there or put the opponent into a losing position. Mark a position as L for losing if the player is forced to put the opponent into a winning position. Q denotes where the queen starts. X is the final position. A winning strategy is to move to one of the L positions reachable from Q.

    Code:
    QLWWWW
    WWWWWW
    WWLWWW
    WWWWWW
    LWWWWW
    WWWWLW
    WWWLWW
    WWWWWX
    Last edited by JakeD; October 22nd 2006 at 06:56 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Chessboard problem. Olympiad question.
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: March 10th 2012, 08:16 AM
  2. Chessboard problem
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: March 31st 2011, 03:47 PM
  3. chessboard problem
    Posted in the Statistics Forum
    Replies: 2
    Last Post: January 5th 2011, 01:00 AM
  4. easy chessboard problem
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: August 23rd 2010, 01:09 PM
  5. chessboard problem
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: January 24th 2009, 06:02 AM

Search Tags


/mathhelpforum @mathhelpforum