Which statement(s) must be true based on the given information?

[some_one]

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 doesn't 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?

 

[arildno]

1. where does willow stand? In particular, what dwarfs or dwarf are next to willo?
2. What propertis must willo have?

 

[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

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 don't know where to start

 

[xtd]

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

 

[some_one]

how do i arrange all this data?
i need to solve such a question in two minutes
and i can't remember every rule
and make conclutions altogether

what parts do i need to write down in order to solve it quickly

??

 

[arildno]

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?

 

[some_one]

he stands in the end
gandolf also in the end because they can't 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

??

 

[arildno]

Since gandolf IS happy, how many properties does he actually share with willo?

 

[xtd]

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.

 

[some_one]

by definition he shares only one with willo

but this shared property could be every property
there are many possibilities

 

[xtd]

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.

 

[some_one]

ooohhh sryy its atleast one property

 

[xtd]

If they share exactly one, they obviously share at least one, don't they? :)

 

[some_one]

they don't have to share only one
but they can share more then one
it gives us many possibilities for the solution

 

[xtd]

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.

 

[some_one]

ohh i understand it now thanks

 

[xtd]

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.

 

[Sakha]

Isn't the question 1 or question 4 also true, I mean, one of those MUST be true, and question 2 Can be true if #4 true.

 

[xtd]

Neither (1) nor (4) has to be true by the given assumptions. One of those is true and one false but none is definitely true - in contrast to (3). And btw, if (4) is true, (2) can not only be true but is.

But as the question is, which one of these has to be true, the answer is (3) and only (3).

Pardon my English, non-native :)

 

[Sakha]

Oh ok, I thought the answer was any possible true.

Im non-native too, so pardon my english

 

[Redbelly98]

For this type of problem, I always make a table first, and try to either fill in or eliminate possibilities from the given information.

In the attached table, I've ordered them Willo, Trillo, and Gandalf to reflect the fact that Willo and Gandalf are not next to each other.
Since we know Willo is not happy, I write "NO" in the corresponding box.
That means Willo must be short and smart, since he has two properties other than happy. I put x's in the corresponding boxes.
Also, since 2 dwarves are happy, Trillo and Gandalf must be happy and I put x's in the corresponding boxes.

Working in this fashion, see if you can either contradict or verify each of the possible answers.