## a logical question..

there three dworfs willo,gandolf,trillo
they are standing one next to the other
data:
two of them are happy
two of them are short
two of them are smart
each dworf has only two properties
for each pair of dworfs that are standing one next to the other they have at least one
common property.
also willo doesnt stand next to gandolf

if we know the willow is not happy
which one of this has to be true?

1.trillo is smart
2.gandolf is smart
3.willo and gandolf share only one property
4.trillo is short

again i need to solve this thing in two minutes
how do i arrange all this data?

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 Recognitions: Gold Member Homework Help Science Advisor 1. where does willow stand? In particular, what dwarfs or dwarf are next to willo? 2. What propertis must willo have?
 they are standing in a line you can arrange them in every way possible as long as you will not cross one of the rules willo must have two properties out of the presented 3 and he must share one property with the dworf close to him all this data make my head spin and i got only two minutes to solve this question i dont know where to start

## a logical question..

Edit: Sorry, didn't see that people are expected to give hints instead of solutions. Some_one, arildno gave you the starting points so just try to answer his questions and keep going from there

 how do i arrange all this data? i need to solve such a question in two minutes and i cant remember every rule and make conclutions altogether what parts do i need to write down in order to solve it quickly ??

Recognitions:
Gold Member
Homework Help
 Quote by some_one they are standing in a line you can arrange them in every way possible as long as you will not cross one of the rules
Precisely!
Does willo stand at one of the ends of the line, or in the middle?

 he stands in the end gandolf also in the end because they cant be together and because willo is not happy which gives us that trilo and gandolf are happy willo ,trilo ,gandolf which gives us many possibilities for sharing the rest of the properties there are so many possibilities even if we think of every possibility for each answer and i have only two minutes to make this whole process ??
 Recognitions: Gold Member Homework Help Science Advisor Since gandolf IS happy, how many properties does he actually share with willo?
 arildno, asking that question is not enough as it only tells us that (3) must be right but not why (1), (2) and (4) are not correct answers [Actually it does, as the question asks 'which one has to be true']. As you - some_one - already stated, the two other properties can be distributed on G and T in which ever way you like, thus neither (1) nor (2) nor (4) have to be true. They could however all be true though not at the same time - if (1) is true, then (2) and (4) are false and vice versa.
 by definition he shares only one with willo but this shared property could be every property there are many possibilities
 It does not matter which property the two share as the given answer (3) only states that they share exactly one property and that has to be true if W has properties a and b and G has properties c and a or b.
 ooohhh sryy its atleast one property
 If they share exactly one, they obviously share at least one, don't they? :)
 they dont have to share only one but they can share more then one it gives us many possibilities for the solution
 No it does not. W definitely is smart and short. That means G and T are both definitely happy. Since two are smart and two are short, either G is smart and T short or vice versa. Therefore W and G share exactly one property, be that smart or short. Edit: To make it clear, I repost my original post: >> two of them are happy >> if we know the willow is not happy Tells us, that G and T are happy. >> each dworf has only two properties Only = Exactly and since W is not happy, he is smart and short. >> each dworf has only two properties Only = Exactly and since G is already happy, he is either smart or short. Therefore he shares exactly (= only) one property with W. >> which one of this has to be true? Tells us, that only one of the given answers is true. As (3) is true, all others are false.
 ohh i understand it now thanks
 Sure. Probably the best way to solve these kinds of puzzles is by trying to categorize the information (which kind of information does a statement give), visualize the dwarves and apply the given information. That may sound hard in two minutes but if you are given so little time, you can expect the solution to be found by simple logic.