Results 1 to 3 of 3

Math Help - Swimmers Medley (Combinations)

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    4

    Swimmers Medley (Combinations)

    Here is a question I have a problem with - I don't know how to find all ansers given restrictions.

    Tayah, Innika, Jessica and Katherine have been selected for a swimming competition. Their coach sets the order they race in, following the conditions.

    i] If Katherine starts, Jessica must go 3rd
    ii] If Tayah or Katherine goes 2nd, Jessica must start.
    iii] Innika runs 2nd if and only if Tayah runs third.
    iv] If Katherine runs 3rd, then Tayah must run second.
    v] Should Katherine run last, then Jessica must run third and Tayah starts.

    List all possible orders which follow the conditions, giving explanations for the solutions.

    Please explain how I should work towards the answer.

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Mar 2008
    Posts
    182
    Quote Originally Posted by jt1894 View Post
    Here is a question I have a problem with - I don't know how to find all ansers given restrictions.

    Tayah, Innika, Jessica and Katherine have been selected for a swimming competition. Their coach sets the order they race in, following the conditions.

    i] If Katherine starts, Jessica must go 3rd
    ii] If Tayah or Katherine goes 2nd, Jessica must start.
    iii] Innika runs 2nd if and only if Tayah runs third.
    iv] If Katherine runs 3rd, then Tayah must run second.
    v] Should Katherine run last, then Jessica must run third and Tayah starts.

    List all possible orders which follow the conditions, giving explanations for the solutions.

    Please explain how I should work towards the answer.

    Thanks
    Well the easiest way to go about it would be to list all possible orders without restrictions...
    I J K T
    I J T K
    I T J K
    I T K J
    I K T J
    I K J T

    J K I T
    J K T I
    J T I K
    J T K I
    J I T K
    J I K T

    K I T J
    K I J T
    K J I T
    K J T I
    K T I J
    K T J I

    T I J K
    T I K J
    T K I J
    T K J I
    T J I K
    T J K I

    Then take, say the first condition and cross out all the ones that contradict it...
    (I don't know how to do the 'spoiler' thing, so I'll just write really small so you can't see it without quoting - assuming you might rather work it out yourself..

    I J K T
    I J T K
    I T J K
    I T K J
    I K T J
    I K J T

    J K I T
    J K T I
    J T I K
    J T K I
    J I T K
    J I K T

    K I J T
    K T J I

    T I J K
    T I K J
    T K I J
    T K J I
    T J I K
    T J K I

    Then the ones that contradict the second condition...

    I J K T
    I J T K

    J K I T
    J K T I
    J T I K
    J T K I
    J I T K
    J I K T

    K I J T

    T I J K
    T I K J
    T J I K
    T J K I

    Then the third...

    I J K T
    I J T K

    J K I T
    J T I K
    J T K I
    J I T K

    T J I K
    T J K I

    Then the fourth

    I J T K

    J K I T
    J T I K
    J T K I
    J I T K

    T J I K

    And finally..

    J K I T
    J T K I
    J I T K

    No guarantee that's correct, mind...

    As for reasons...
    They're the only ones that satisfy all conditions..?

    Or you could just write out all the possibilities, and mark which number condition they contradict...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2009
    Posts
    4
    thanks a lot

    yes you were right, i did want to work it out myself, and your 'whited out' answer was also very useful for me to not 'accidentally' cheat.

    I will try work it out myself and compare with yours.

    Thanks again
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Combinations
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: January 25th 2010, 09:00 PM
  2. combinations
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: January 22nd 2010, 02:50 PM
  3. Combinations
    Posted in the Statistics Forum
    Replies: 1
    Last Post: January 21st 2010, 02:33 PM
  4. combinations
    Posted in the Statistics Forum
    Replies: 1
    Last Post: September 9th 2008, 03:44 PM
  5. combinations
    Posted in the Advanced Statistics Forum
    Replies: 11
    Last Post: September 4th 2008, 10:26 PM

Search Tags


/mathhelpforum @mathhelpforum