Which one of the following could be the order, from first to last, in which the valves are opened?

Christopher on June 6, 2018

@Madelyn-Luskey

This is a linear game, so you're going to need to set up the game like so:
_ _ _ _ _ _ _ _
1 2 3 4 5 6 7 8

And begin applying rules.

1. K&P _ _ _ _ _ _ _ _
1 2 3 4 5 6 7 8
H H K
P
2. H _ _ _ _ _ _ _ _
1 2 3 4 5 6 7 8
H H O L K K K
O O L P P P
L L H H
O
3. G _ _ _ _ _ _ _ _
1 2 3 4 5 6 7 8
H H O L L K K K
O O L P P P
L L H H
O
G
4. N _ _ _ _ _ _ _ _
1 2 3 4 5 6 7 8
H H H O L K K K
O O O L P P P
L L L N H H
L N O
G
N

5. K _ _ _ _ _ _ _ L/I
1 2 3 4 5 6 7 8
H H H O L K K K
O O O L K P P P
L L L N H H
I L N O
G
N
With all of that you can determine that 8 will be either L or I, which can make evaluations faster.

Christopher on June 6, 2018

Question 1. This asks for a full "possible" hypothetical. Start with the fact that 8 must be I or L, and you can eliminate (D). Then hit your rules. #1 require K&P ahead of H, and they're all fine. #2 is H
_ _ _ _ _ _ _ L/I
1 2 3 4 5 6 7 8
H H H O L K K K
O O O L K P P P
L L L N H H
I L N O
G
N
1.K I N G P H O L

Christopher on June 6, 2018

Question 2 asks for which of the answers COULD NOT be the fifth valve. If you've diagrammed correctly, it's clear that K is not an option for 5, so you've got the answer immediately.

Christopher on June 6, 2018

Question 3 imposes the hypothetical that "I" be the second valve opened.

Keeping in mind the diagram and rules, there are a couple things you can deduce immediately. If "I" is 2, then L must be 8, since it's the only other option. K must also be 1 because K must come before "I" as per rule #5. So you have:

K I _ _ _ _ _ L

At this point you can either start with rules or start eliminating answers. I usually go for the answers. So (A) puts G in 3. The only thing we know about placing G is that it comes before L, so it could be wide open. (B) puts H in 4. H must have K, P, and N ahead of it, so with K in 1, and "I" in 2, the earliest that H can come in is 5. (B) is impossible within the "I" in 2 hypothetical and therefore is the answer. I would add the partial hypothetical below your diagram.

_ _ _ _ _ _ _ L/I
1 2 3 4 5 6 7 8
H H H O L K K K
O O O L K P P P
L L L N H H
I L N O
G
N
1.K I N G P H O L
3.K I _ _ _ _ _ L

Christopher on June 6, 2018

Question 4 adds the condition that L is 7. This means "I" must be 8 as it's the only other option. Therefore, (B) is the clear answer.

Christopher on June 6, 2018

Question 5 also depends on your fully diagramming the rules. You'll need to eliminate each answer based on the diagram.

(A) P can be in position 1, so this does not have to be true.

(B) G can also be in position 1, so this does not have to be true.

(C) O cannot be opened until four other valves are opened, so this statement is actually false.

(D) H can be opened 4th, meaning four valves can be opened afterwards, so this does not have to be true.

(E) The last position that N can be in is 5, meaning that, at most, only four valves can precede N, and this answer must be true.

Christopher on June 6, 2018

Question 6 puts K in position 4. We know two major things about K. K
So (A) is eliminated as I cannot come before K.

(C) is eliminated because there's not room for G after K.

(D) is eliminated because H must come before O, meaning 6 is the earliest position O can take.

(E) is eliminated because there is no room for P after K in this hypothetical.

Therefore (B) is the only possible answer.

Christopher on June 6, 2018

Question 7 places G in position 1 and "I" in position 3. Given rule 5, K must then be in 2. Since H always has K, P, and N ahead of it, by having G and I ahead, the earliest position it can be is 6, and O and L must immediately follow. So, by putting G in 1 and "I" in 3, you can determine everything except whether N or P is in 4 or 5.

G K I N/P N/P H O L

(A) must be true
(B) can be true but can be false
(C) must be true
(D) must be true
(E) must be true

Therefore (B) is the answer. Even though it could be true, the others MUST be true, and that's what the question asks you to evaluate.

I hope this clears up the game for you.

Let me know if you have questions.

hkolon on May 29, 2020

@Christopher, in your diagramming, can you explain how you are writing out the rules? I don't think I understand your system. Specifically, I'm trying to figure out how you knew K could not be the fifth valve from your diagramming. Thanks!

Anna20 on June 9, 2020

Hi @Christopher - I tried to diagram this making a diagram using the relationships (e.g. using the <, > as I remembered from the sequencing lecture) - would you doing recommend this for this question, as initially all the rules are relationship between variables? If you were doing this method, would you be able to show how to correctly diagram the rules? Many thanks!