Results 1 to 3 of 3

Math Help - Problem Solving

  1. #1
    Junior Member
    Joined
    Feb 2008
    From
    Victoria
    Posts
    39

    Problem Solving

    Three bags:Each bag contains 2 apples. 2 green in one, 2 red in another and one of each colour in third bag. All 3 bags are mislabelled. You may look at only one apple from any one of the bags. Which bag should you select from to be sure you can determine the content of all three bags.
    Last edited by not happy jan; May 17th 2008 at 12:01 AM. Reason: Queston 1 answered
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member wingless's Avatar
    Joined
    Dec 2007
    From
    Istanbul
    Posts
    585
    \sqrt{2.25}

    You know that 2.25 = \frac{225}{100}

    \sqrt{\frac{225}{100}}

    \frac{\sqrt{225}}{\sqrt{100}}

    I think you can do it now.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,547
    Thanks
    539
    Hello, not happy jan!

    This is a classic (very old) problem . . .


    Three bags: each contains two apples.
    Two green apples in one, two red apples in another, and one of each colour in the third.
    All 3 bags are mislabeled. You may look at one apple from any one of the bags.
    Which bag should you select from to determine the contents of all three bags.

    The key is that the bags have the wrong labels.

    The bags look like this: . \boxed{\text{G/G}} \quad \boxed{\text{R/R}} \quad \boxed{\text{G/R}}



    Take an apple from the bag labeled \boxed{\text{G/R}}


    Suppose it is Green. .
    We can reverse the argument later.
    Since it is not the G/R bag, it must contain \text{G/G}.

    . . We have: . \begin{array}{c|c|c|c|}<br />
\text{Labels} & \boxed{\text{G/G}} & \boxed{\text{R/R}} & \boxed{\text{G/R}} \\ \hline<br />
\text{Contents} & & & \text{G/G} \end{array}



    Where is the \text{R/R} bag?
    Since it is not the one labeled \boxed{\text{R/R}}, it is the one labeled \boxed{\text{G/G}}

    . . We have: . \begin{array}{c|c|c|c|}<br />
\text{Labels} & \boxed{\text{G/G}} & \boxed{\text{R/R}} & \boxed{\text{G/R}} \\ \hline<br />
\text{Contents} & \text{R/R} & & \text{G/G} \end{array}



    Finally, \boxed{\text{R/R}} contains \text{G/R}

    . . Therefore: . \begin{array}{c|c|c|c|}<br />
\text{Labels} & \boxed{\text{G/G}} & \boxed{\text{R/R}} & \boxed{\text{G/R}} \\ \hline<br />
\text{Contents} & \text{R/R} & \text{G/R} & \text{G/G} \end{array}


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    This problem can be made even more baffling like this . . .


    . . One bag contains 11 green apples.
    . . One bag contains 13 red apples.
    . . One bag contains 7 green and 8 red apples.

    The bags are labeled: . \boxed{\text{Green}},\;\boxed{\text{Red}},\;\boxed  {\text{Mixed}}
    . . but each bag is incorrectly labeled.

    You may draw one apple from any bag,
    . . examine its color, and set it aside.
    You may repeat this sampling process.

    What is the least number of samples you must take
    . . to determine the contents of each bag?


    The solution is the same:
    . . Take one from the bag labeled "Mixed".

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help solving a problem.
    Posted in the Algebra Forum
    Replies: 0
    Last Post: August 13th 2011, 06:37 AM
  2. Problem Solving #1
    Posted in the Number Theory Forum
    Replies: 11
    Last Post: November 3rd 2010, 07:30 PM
  3. Further Problem Solving
    Posted in the Algebra Forum
    Replies: 3
    Last Post: March 18th 2010, 03:42 AM
  4. Problem Solving
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 19th 2008, 04:56 PM
  5. Need help in solving a problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 18th 2008, 04:02 AM

Search Tags


/mathhelpforum @mathhelpforum