Q8

[kwjustin89]

I initially bombed this game, although got most of the set up and inferences. When I came back to redo the game untimed, I managed to bulldoze through most of them (and understand them) but feel uneasy about this approach. For most (8-13, excluding 11 & 12), it seemed that there was no other way but to start trying each answer choice, which can be time consuming obviously. Am I missing something else in the game, rules, or inferences? I apologize if this is a really broad question.

[giladedelman]

Thanks for posting!

It does sound like you're missing some inferences, but I can't tell for sure because you didn't tell me what you figured out. Can you show or explain your set-up/inferences to me?

[kwjustin89]

My initial set up was similar to the one provided here. I did initially miss the Y -> P inference and the Y, G, O < 3 inference. However I redid the game once I had the correct set up and still had the described issues.

For instance, on #8; I got the answer correct after trying 4 different hypotheticals. Even given the correct inferences, I just am not seeing a faster way...and the same applies to the later questions. Thanks so much for your help!

[giladedelman]

Thanks for the follow-up.

You're right that trying out answer choices is slow and should be avoided as much as possible. But I think there are better ways to deal with this game.

Let's look at number 8. This is an unconditional "must be false" question. On these unconditionals, remember our mindset: defer judgment. Instead of trying out each answer choice, let's defer on ones that don't seem obviously correct, with the knowledge that most of the time the right answer will be pretty easy to spot.

In this case,

(A) - looks fine, defer.
(B) - looks fine, defer.
(C) - aha! This can't work, because we know from our setup that each window must have either P or O. So G and R, with nothing else, violates that rule. This is our answer.

Now, on the conditional questions, our mindset is to follow the inference chain all the way. Let's look at number 10, for example:

The complete color combo in one window is P, R, O. So we start with

1: P R O
2: G P ?
3: ?

Okay, now we know we have to have Y somewhere. It can't go in 1 or 2 (I assigned the windows arbitrary numbers just for my sanity), so it has to go in 3. And if Y is there, P also has to be there:

1: P R O
2: G P ?
3: Y P ?

And since we know we need two R's, one of those question marks will be an R:

1: P R O
2: G P R/
3: Y P /R

Okay, we've followed the inference chain about as far as we can. Now let's take a look at the answers. What could be the complete combo in one of the other windows?

(A) doesn't work; the window with G also has to have P.

(B) looks good: window 2 could have O in addition to G and P.

(C) is out, we need P and G/Y.

(D) is out because we still need G or Y.

(E) is incorrect because the window with G needs to have P.

So (B) is the only one that works; that's the correct answer.

Does that help at all? With the unconditional question, we deferred judgment until we found an answer that clearly violated a rule. On the conditional question, we inferred everything we could before looking at the answer choices.

[yoohoo081]

Okay, I'm having serious problem with why C is the right answer.

I understand why P or O has to be in the argument.
However, isn't D also CANNOT be possible since P & O cannot be in a condition together?!

I know #10 gives a combination with P & O together, but this is #8. Can you explain how C is a better answer when D just completely goes against our given condition please?

[farhadshekib]

Okay, I'm having serious problem with why C is the right answer.

I understand why P or O has to be in the argument.
However, isn't D also CANNOT be possible since P & O cannot be in a condition together?!

I know #10 gives a combination with P & O together, but this is #8. Can you explain how C is a better answer when D just completely goes against our given condition please?

P and O can be together.

The rules simply tell is the following:

If you don't have P, then you must have O.

If you don't have O, then you must have P.

That is, either P or O (or both) must be present in each of the three windows.

Had the rule stated: if a window does not have P, then it must have O (but not both), you'd be correct.

[Carlystern]

The answer (C) is makes me want to slap myself. It's like hiding in plain sight. I sure hope others have overlooked the fact that the absence of O implies the presence of P and vice versa. P or O HAS to be in each window. This makes me want to slap myself really hard!

I wish Ray Kurzweil would just invent the right nanotechnology so I can implant GOOGLE into my brain!!!!

[Carlystern]

Also, this rule doesn't imply that a window couldn't have, both, P & O, right?

It says: ~P-->O or ~O-->P

It doesn't mean that you can't have both, right?

[tommywallach]

Absolutely right, Carly. And I'll talk to Ray about getting that chip installed in your brain...