Q23

[marcus.v.p.]

Can some one explain the best setup and process for number 23 and how the answer is B?

Thank you!

[ohthatpatrick]

First of all, in case you haven't yet heard this from someone else, this is one of the worst games ever. The circular setup is just a really tough variable to deal with.

We either have the option of representing the diagram in a circular fashion (which has the advantage of being visually meaningful but the disadvantage of being totally unfamiliar) or we can represent the diagram horizontally (which has the advantage of being familiar but the disadvantage of being non-circular, forcing us to adapt and think a little harder about what we're doing).

Since I have no means to do the circular version of the diagram in this typing environment, we'll do the horizontal way.

Diagram:
(last) __ __ __ __ __ __ __ __ (first)

All I mean by "last" and "first" is a reminder that the 1st spot is next to the 8th spot and vice versa.

I'd put rule 1 in the diagram.
(last) F __ __ __ G __ __ __ (first)

Rule 2: OI
Rule 3: ~(HK), ~(HF)
(parentheses are like a cloud around HK, saying to me "I don't want to see HK touching in either order")

Q23 gives us this limitation: K _ _ _ I or I _ _ _ K

When we get a new rule on a conditional "If" question, we start by attaching our old rules to this, so we get
K _ _ O I or O I _ _ _ K

(in reality, these are the same ... they just look different because we're representing a circular layout horizontally)

And we might notate that H can't go before or after the K.

Let's think about where we could put K _ _ O I into our diagram:

(last) F __ __ __ G __ __ __ (first)

We can't put the K on 2 or else the OI would overlap with G. We can't put the K on 5 or 6 or else the OI would overlap with F. So we can put K on 3, 4, 7, or 8 it seems.

(last) F __ K __ G O I __ (first)
(last) F __ __ K G __ O I (first)
(last) F O I __ G __ K __ (first)
(last) F __ O I G __ __ K (first)

Who's left? H, M, P

M and P are free agents, meaning we can put them anywhere. But H can't be next to F or K.

That means that the first scenario is impossible. There's no place to put H. Spots 2, 4, and 8 are all next to F, K, or both.

If we're really being savvy, we might recognize at this point that since the OI chunk can't go next right after G, then (B) will be our correct answer.

If we don't see that, we'll cross off that unworkable top scenario and focus on the next three:
(last) F __ __ K G __ O I (first)
(last) F O I __ G __ K __ (first)
(last) F __ O I G __ __ K (first)

In each case, the placement of H is determined by needing to keep it away from F and K. M and P just fill in the gaps.

(last) F (m, p) K G H O I (first)
(last) F O I H G m/p K p/m (first)
(last) F m/p O I G H p/m K (first)

So, from these, who can go next to O? H, I, F, M, P

Cross off (A), (C), (D), and (E)

Hope this helps.

[marcus.v.p.]

Good stuff!!! Thank you!

[kkate]

First of all, in case you haven't yet heard this from someone else, this is one of the worst games ever. The circular setup is just a really tough variable to deal with.

Does this mean I should not be overly concerned about this particular question? I spent half of my day trying different methods to approach this question to see which method works best for me (specifically, I was much more comfortable with number line first then after 9999 attempts at the question and looking through solutions, I realized the question solves much better with a circular diagram.) Should I just move on even though I still feel like I'll most likely spend too much time on similar questions like this if it were to come up on the exam?

Thanks,
Kate

[tommywallach]

That is pretty difficult to say. I mean, usually by the time you can tell something is crazy hard, you're already in it, you know? But yes, if you do notice that something is INSANE, skip that thing!

-t