Could someone explain this logic problem to me?

Cafe Society
1

I’m playign through Star Wars: KotOR and there is one part in the game where you have to fix a droid.

The puzzle says that there are three nodes, two of which are not reporting correctly. To fix the droid’s particular system you have to choose the node that is reporting correctly. The nodes read as follows:

Node 1 reports node 2 is malfunctioning.

Node 2 reports node 3 is malfunctioning.

node 3 reports node 2 is malfunctioning.

Through trial and error I found out that the correct answer is that Node 2 isreporting correctly.

But come someone explain how one can arrive at that conclusion?

And if you have similar logic examples please link or type them! I might suck at them but their intriguing!

2

If Node 2 is malfunctioning, both Node 1 and Node 3 are reporting correctly; but only 1 node is reporting correctly; therefore Node 2 is not malfunctioning.

3

Alright, you know that exactly two are reporting incorrectly, right? Out of the three, one of them, by default, has to be either 1 or 3. Since 1 and 3 are reporting the same thing, it’s impossible for one to be right and the other wrong.

Simple way to look at it- the correct one can’t be 1 or 3, because then the other one would be correct too. Only one can be functioning properly, so it has to be the unique one.

4

Let’s run it down. We have to assume that ‘malfunction’ in this situation is the same as ‘is always wrong.’ Only one of the nodes is functioning, so there are three outcomes:

a) Node 1 is functioning. Thus Node 2 is malfunctioning. Then Node 2 must be incorrect, so Node 3 is really functioning. However, Node 3 cannot be functioning because Node 1 is functioning and we can only have one at a time.

b) Node 2 is functioning. Thus Node 3 is malfunctioning. Thus Node 3 is incorrect, and Node 2 is really functioning. Node 1 is also malfunctioning, so it is also incorrect and Node 2 is functioning.

c) Node 3 is functioning. Thus Node 2 is malfunctioning. Thus Node 2 must be incorrect, so Node 3 is functioning. So far so good. However, Node 1 must also be incorrect, which means that Node 2 is functioning. Node 2 can’t be both correct and incorrect at the same time.

The case in which Node 2 is the functioning one is the only one in which we don’t run into any conflicting statements.

5

HAHAHA!

So simple!

I guess my mind din’t make the important distinction that only ONE of the nodes is correct.

Thanx a lot guys!

6

Assume that node 1 is correct. Then node 2 is lying. Then node 3 is lying. Then node 2 is telling the truth. But, node 2 is lying. We have a contradiction.

Assume that node 3 is correct. Then node 2 and node 1 are lying. If node 1 is broken, node 2 works. But, node 2 is lying. Contradiction again.

Assume node 2 is correct. 2 says 3 is broken. 3 (reversed) says 2 is working. 1 (reversed) says that 2 is working. It works.

Trifurcation ain’t pretty, but it works in this case.

7

I can put it another way.

We know that only one is working and two are not.
So if you would write them down and put a check next to one, and and x next to the other two, then you could see if each node’s “reports” are correct.

√ 1. “Node 2 doesn’t work”
x 2. “Node 3 doesn’t work”
x 3. “Node 2 doesn’t work”

So, if node one is infact working, then it means node 2 doesn’t work. Okay, we’ll take it at it’s word, so two actually means that 3 IS working. Well, looking at your marks, 3 shouldn’t be working so it doesn’t fit the established pattern.

Result… Node 1 is not working.

TRY AGAIN
x 1. “node 2 don’t work”
√ 2. “node 3 don’t work”
x 3. “node 2 don’t work”

If node 2 is working, it means node 3 isn’t working. That’s good so far. So then, if node 3 isn’t working, it means node 2 is working. That checks out… Node 3 must be wrong. . . . The only one left, node 1, must not be working either. So, it means that node 2 is working. . . well, that checks out with our x’s and checks.

ALL CHECKS/MARKS are not contradicting… so we found that node two is working.

But in all fairness, to do a complete and thorough job, you should do another scenario were node 3 has the check next to it.

x 1. “node 2 don’t work”
x 2. “node 3 don’t work”
√ 3. “node 2 don’t work”

So… if 3 is right, two is wrong… if 2 is wrong, it means 3 is right. This checks out so far. Only one left… if 1 is wrong, then 2 is right… that contradicts what 3 says… so the answer, w/o a doubt is NODE 2 IS WORKING.

THIS is a form of logic that I have been accustomed to. (along with ending sentences in prepositions) :o

8

I think the question’s pretty much answered, but I just want to throw this out there. If you write it like this, it might be easier.

(1) = (2) is false.
(2) = (3) is false.
(3) = (2) is false.

or even

(1) = ~(2)
(2) = ~(3)
(3) = ~(2)

where ~ means “not” or “the following is false”