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A logical question

  1. Aug 19, 2008 #1
    in a zoo there are
    2 wolfs
    2 tigers
    2 lions
    2 sheep
    we need to house them in four cages (two animals in each cage) by these rules:
    A.in one cage we need to house a wolf and a sheep.
    B.we cant house two animals of the same kind in one cage.

    which one of these arguments in necessarily true:
    1.at least in one cage a lion and a tiger will be housed.
    2.at exactly one cage a lion and a sheep will be housed.
    3.at exactly one cage a tiger and a sheep will be housed.
    4.there is another cage in which a sheep and a wolf will be housed.

    what is the simplest way to solve this question??

    i found one combination for each argument
    and tried to find common stuff between them.

    regarding answer 1:
    |wolf ,sheep |lion,tiger|sheep,lion|wolf,tiger|

    regarding answer 2:
    |wolf,sheep |sheep,lion|wolf ,tiger|lion,tiger|

    regarding answer 3:
    |wolf,sheep |sheep,tiger|wolf ,lion|lion,tiger|

    regarding answer 4:
    if we put a fifth cage it leaves us with 4 animals
    we cant put two animals in each one of the four left cages
    if we left with only fours animals,so its not possible.

    i found that a lion and a tiger in one cage is the common thing among these three combinations.

    but i cant think of three combination in order to solve this kind of question
    it takes too much time.

    is there any easier way??
  2. jcsd
  3. Aug 19, 2008 #2
    1 sheep is with 1 wolf. They're gone. No need to worry about them. So you have

    1 sheep
    2 tigers
    2 lions
    1 wolf

    To me, it's obvious right away that a lion needs to be a tiger. Anyways, if you it isn't for you, or you want to argue it, then do the following: pick an animal with 2 individuals, lion or tiger here. I choose tiger. Do the following

    Tiger ___ | Tiger ___ | ___ ___

    You have the fill in the blanks with the remaining animals. Since 2 lions cannot be put together, they cannot be put in the last section, to the right. Therefore at least one must be put on the left, with a tiger.
  4. Aug 20, 2008 #3
    i understand that
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