# A logical question

1. Aug 12, 2008

### 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 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?

2. Aug 12, 2008

### arildno

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

3. Aug 12, 2008

### 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 dont know where to start

4. Aug 12, 2008

### 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

Last edited: Aug 12, 2008
5. Aug 12, 2008

### some_one

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

??

6. Aug 12, 2008

### arildno

Precisely!
Does willo stand at one of the ends of the line, or in the middle?

7. Aug 12, 2008

### some_one

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

??

8. Aug 12, 2008

### arildno

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

9. Aug 12, 2008

### 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.

10. Aug 12, 2008

### some_one

by definition he shares only one with willo

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

11. Aug 12, 2008

### 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.

12. Aug 12, 2008

### some_one

ooohhh sryy its atleast one property

13. Aug 12, 2008

### xtd

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

14. Aug 12, 2008

### some_one

they dont have to share only one
but they can share more then one
it gives us many possibilities for the solution

15. Aug 12, 2008

### 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.

Last edited: Aug 12, 2008
16. Aug 12, 2008

### some_one

ohh i understand it now thanks

17. Aug 12, 2008

### 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.

18. Aug 12, 2008

### 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.

19. Aug 12, 2008

### 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 :)

20. Aug 12, 2008

### Sakha

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

Im non-native too, so pardon my english