Results 1 to 8 of 8

Math Help - Coin problem

  1. #1
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,802
    Thanks
    692

    Coin problem



    Nine coins are placed in 8 rows of 3 coins each.


    \begin{array} {ccccc}<br />
O &\to& O &\to& O \\<br />
\downarrow & \searrow & | & \swarrow & \downarrow\\<br />
O &\to& O &\to& O \\<br />
\downarrow & \swarrow & \downarrow & \searrow & \downarrow  \\<br />
O &\to& O &\to& O  \end{array}



    Move two coins and form 10 rows of 3 coins each.


    Follow Math Help Forum on Facebook and Google+

  2. #2
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Is that 8 supposed to be a three? I'm not very good at this stuff, could you explain how there can be nine coins in 8 rows of three.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by VonNemo19 View Post
    Is that 8 supposed to be a three? I'm not very good at this stuff, could you explain how there can be nine coins in 8 rows of three.
    "Row" here doesn't just mean a horizontal row, it refers to any three coins that are in a straight line. So there are three horizontal rows, three vertical rows and two diagonal rows.

    Spoiler:
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,110
    Thanks
    68
    How about 11 rows:
    1 2 3
    4 5 6
    7 8 9
    Put 4 and 6 on top of 5; then you have:
    1 2 3
    7 8 9
    1 4 9
    1 5 9
    1 6 9
    2 4 8
    2 5 8
    2 6 8
    3 4 7
    3 5 7
    3 6 7

    James F. Fixx: "everything that's not implicitly prohibited in a puzzle is allowed"
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by Wilmer View Post
    How about 11 rows:
    1 2 3
    4 5 6
    7 8 9
    Put 4 and 6 on top of 5; then you have:
    1 2 3
    7 8 9
    1 4 9
    1 5 9
    1 6 9
    2 4 8
    2 5 8
    2 6 8
    3 4 7
    3 5 7
    3 6 7

    James F. Fixx: "everything that's not implicitly prohibited in a puzzle is allowed"
    You're assuming that the coins have no thickness.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,110
    Thanks
    68
    Quote Originally Posted by Opalg View Post
    You're assuming that the coins have no thickness.
    Mr Fixx says that ok !
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,802
    Thanks
    692
    This is the standard solution:

    Spoiler:

    \begin{array}{ccccccccc}<br />
A & \to & \to & \to & B & \to & \to & \to & C \\<br />
& \searrow && \swarrow & | & \searrow && \swarrow \\<br />
& & D & \to & E & \to & F \\<br />
& \swarrow && \searrow & | & \swarrow && \searrow \\<br />
G & \to & \to & \to & H & \to & \to & \to & I \\<br />
\end{array}


    Plus rows AEI and CEG.

    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,110
    Thanks
    68
    Ok, Soroban.

    But if 11 instead of 10, do you agree mine is "acceptable"?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. coin problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 19th 2010, 08:33 AM
  2. Coin problem
    Posted in the Statistics Forum
    Replies: 1
    Last Post: February 5th 2010, 12:07 PM
  3. Coin problem.
    Posted in the Statistics Forum
    Replies: 1
    Last Post: April 1st 2009, 03:51 AM
  4. Coin Problem
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: March 18th 2009, 08:44 AM
  5. Coin problem
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 21st 2009, 01:20 AM

Search Tags


/mathhelpforum @mathhelpforum