A logical question

1. Aug 19, 2008

some_one

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.

|wolf ,sheep |lion,tiger|sheep,lion|wolf,tiger|

|wolf,sheep |sheep,lion|wolf ,tiger|lion,tiger|

|wolf,sheep |sheep,tiger|wolf ,lion|lion,tiger|

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. Aug 19, 2008

Werg22

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.

3. Aug 20, 2008

some_one

thanks
i understand that