Results 1 to 3 of 3

Math Help - No of ways ?

  1. #1
    Junior Member
    Joined
    Mar 2010
    Posts
    52

    No of ways ?

    \\\textup{In how many ways can one fill a 4X4 matrix with }\pm1\\
    \textup{so that the product of the entries in each row and each column is equal to -1 ?}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by banku12 View Post
    \\\textup{In how many ways can one fill a 4X4 matrix with }\pm1\\
    \textup{so that the product of the entries in each row and each column is equal to -1 ?}

    This doesn't seem a hard problem, does it? It can be long and annoying, but the algorithm to follow seems very clear: in every row-column there must be either 1 or three -1's...well, try some combinations by yourself .

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,959
    Thanks
    1783
    Awards
    1
    Quote Originally Posted by banku12 View Post
    \\\textup{In how many ways can one fill a 4X4 matrix with }\pm1\\
    \textup{so that the product of the entries in each row and each column is equal to -1 ?}

    Put a + in each column in such that no row has more than one +.  \begin{array}{*{20}c}    -  &  +  &  -  &  -   \\    -  &  -  &  -  &  +   \\    +  &  -  &  -  &  -   \\    -  &  -  &  +  &  -   \\ \end{array} .
    That is one way to do this. And that can be one of 4!=24 ways.
    Now, change each + to and each to plus. How many ways do you have?

    Suppose we use 6 +s and 10 s. \begin{array}{*{20}c}    +  &  -  &  -  &  -   \\    +  &  +  &  +  &  -   \\    +  &  -  &  -  &  -   \\    -  &  -  &  -  &  +   \\ \end{array}
    How many ways can we rearrange the columns and rows? Be careful of duplications.
    Again change the +s and s.

    Is there another possible scheme?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How many ways
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: September 23rd 2011, 11:01 AM
  2. How many ways...
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: September 22nd 2010, 01:30 PM
  3. No. of Ways....
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: September 1st 2009, 08:43 PM
  4. how many ways could you
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: February 25th 2008, 06:10 PM
  5. in how many ways can...
    Posted in the Statistics Forum
    Replies: 2
    Last Post: May 13th 2007, 08:37 AM

Search Tags


/mathhelpforum @mathhelpforum