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## Setup and Rule Diagrams

• PowerScore Staff
• Posts: 8930
• Joined: Feb 02, 2011
#28485
Complete Setup and Rule Diagram Explanation

This is a Basic Linear Game: Balanced, Identify the Templates.

The key to this game is to use the last rule to create the two mutually exclusive sequences that control this game.

From the game scenario, we know the following linear scenario underpins the sequences:
Because there are no ties, this is a balanced game, wherein each of the six hotel suites is assigned to a different space.

Ultimately, the final rule controls the game , and students who begin diagramming before reading all of the rules often find themselves scrambling to re-diagram. Remember, always read the entire scenario and accompanying rules prior to starting your diagram.

For the purpose of clarity, let’s review each rule individually. At the conclusion of showing the diagram for each rule, we will combine the diagrams into two super-sequences.
• Rule #1. This is a basic sequential rule:

H L

Rule #2. This is a conditional rule, and the sufficient condition is that G is more expensive than H. When that occurs, then J is more expensive than both K and L:
Rule #3. This is another conditional rule, and the sufficient condition is that H is more expensive than G. When that occurs, then K is more expensive than both J and L:
Rule #4. Initially this rule seems like a simple either/or rule, where F is either more expensive than G (diagrammed as F G) or F is more expensive than H (diagrammed as F H). However, the “but not both” portion of the rule means that F is more expensive than only one of G or H at a time, and since there are no ties, that means that the other variable must be more expensive than F. So, when F is more expensive than G, then H must be more expensive than F, producing the following sequence:

H F G

And, when F is more expensive than H, then G must be more expensive than F, producing the following sequence:

G F H

Every game solution must conform to one of the two sequences produced by rule #4, and thus you should take those two base sequences and create two templates for the game.
Sequence Template #1

This template is produced by the part of rule #4 that produces the H F G sequence. To build a super-sequence that captures the relationship between all six hotel suites, first add rule #1 to the sequence:
The next step is to add rule #3 to the sequence (rule #2 does not apply to this sequence, and can be ignored). This step is more difficult than the first step above, because adding the third rule creates an unwieldy diagram:
The relationship between K, J, and L is clear when isolated in rule #3, but when added to a sequence where L is already less expensive than another hotel suite, H, the relationship is a bit more difficult to diagram. In the above diagram, K and H have no relationship other than both being more expensive than L.

The tricky part comes in analyzing the relationship between H and J, and between K and F G. In both instances, there is no relationship. That is, J can be more or less expensive than H, and K can be more or less expensive than both F or G. Of course, this difficulty in representation and analysis is exactly what the test makers intended.

To better understand the possibilities inherent in this sequence, consider the following hypotheticals, all of which are valid:
• Hypothetical 1: K - H - F - G - J - L
Hypothetical 2: K - J - H - L - F - G
Hypothetical 3: H - F - G - K - L - J
Hypothetical 4: H - F - K - J - G - L
Hypothetical 5: H - K - L - F - G - J
Also, remember to use the Sequencing Diagramming Guidelines, and consider which variables can be first and which can be last. In the sequence above, only K or H can be first, and only G, J, or L can be last.

Sequence Template #2

This template is produced by the part of rule #4 that produces the G F H sequence. To build a super-sequence that captures the relationship between all six hotel suites, first add rule #1 to the sequence:
• G F H L

The next step is to add rule #2 to the sequence (rule #3 does not apply to this sequence, and can be ignored). This step is more difficult than the first step above because adding the second rule creates a slightly unwieldy diagram:
The relationship between K, J, and L is clear when isolated in rule #2, but when added to a sequence where L is already less expensive than three other hotel suites, the relationship is more difficult to diagram (although not as troubling as the first sequence template). The tricky part comes in analyzing the relationship between J and K and the other variables. J must be more expensive than K and L, but J has no relationship with G, F, or H. Similarly, K must be less expensive than J but otherwise K has no relationship with any other variable in the chain. Analyzing which variables can be first and which can be last in the sequence above, only G or J can be first, and only K or L can be last.

To better understand the possibilities inherent in this sequence, consider the following hypotheticals, each of which is valid:
• Hypothetical 1: G - F - H - J - L - K
Hypothetical 2: J - K - G - F - H - L
Hypothetical 3: J - G - F - H - L - K
Hypothetical 4: G - J - F - K - H - L
Hypothetical 5: G - F - J - H - K - L
Combining all of the information above leads to the following optimal setup for the game:
Use the two sequence templates to answer the questions.
srcline@noctrl.edu
• Posts: 243
• Joined: Oct 16, 2015
#24525
Hello

So I am using the LG Bible when I was doing this game. So you would do two templates b/c of the last rule that splits the game into either

H>F>G (when F is more expensive than G)
and

G>F>H (when F is more expensive that H)

So when in a sequencing game when there is a rule like # 4 can you assume that there will be two templates?

After this point I'm lost. I understand that you cant add rule 2 do the H>F>G diagram but I am having a hard time figuring out how to diagram the remaining rules.

Also for the 2nd temp. wouldn't J go on top of the sequence b/c the 2nd rule states that J has to be more expensive that J or L?

Thankyou
Sarah
Nikki Siclunov
• PowerScore Staff
• Posts: 1362
• Joined: Aug 02, 2011
#24626
Hi Sarah,

Usually, yes - when a rule establishes two mutually exclusive, and collectively exhaustive possibilities (H -- F -- G or else G -- F -- H), these possibilities will likely lead to the creation of two separate sequencing chains. This is especially true here, because the second and the third rules link to each of these two possibilities directly:
• The first possibility listed above triggers the sufficient condition of the third rule;
The second possibility listed above triggers the sufficient condition of the second rule.
Consequently, each of these two possibilities must be connected to the necessary conditions of the third and second rules, respectively. After we factor in the first rule, the two sequencing templates therefore look like this:
srcline@noctrl.edu
• Posts: 243
• Joined: Oct 16, 2015
#24955
Hello Nikki

Okay, I think I get the diagram now. I went back and looked at temp.2 and it makes sense why G or J could be first b/c we don't know their relationship. Also I get why we wouldn't add the third rule to the temp 2. b/c its not relevant either.

Sarah
Imcuffy
• Posts: 17
• Joined: Aug 19, 2020
#80626
Hi,

I am having some trouble diagramming your rule that states: F is more expensive than G, or else F is more expensive than H, but not both.

My diagram was a branch sequence.

Your diagram was: H--F--G or G--F-H.

I am confused as to when to diagram it as a branch and when to diagram it as a sequence. The reason I diagrammed it as a sequence was because on pg. 449 (Mutually Exclusive Outcome) in their example: "Either R is taller than S, or else R is taller than T, but not both" you used a branch sequence. Further, in the Conditional Sequencing Diagramming Drills, in #6 (pg. 454) you also used a branch sequence.

So, I just am not clear on when do I use the branch sequence and when do I use a basic sequence in "but not both" questions. Also, could you tell me how to upload screenshots on here. When I tried to paste it, nothing showed up. This would be much easier than having to write out on paper what you wrote in the book, to then have to take a picture of it, send it to my email, download it from email, than upload it as an attachment on this thread.

update: After doing all of those steps to upload the picture, the thread is not allowing me to do so because it states that it is to large of a file.

Thanks,
Stephanie Oswalt
• PowerScore Staff
• Posts: 849
• Joined: Jan 11, 2016
#80648
Hi Imcuffy!

Thanks for your post. I have moved your question to the thread discussing this game. Please review the above explanation and the following discussion, and see if that helps!

Thanks!
frk215
• Posts: 33
• Joined: Sep 07, 2020
#94951
Hello!

I found this game super confusing because I tried to chart out the contrapositives of the conditional chains. the result of this was a mess that didn't even allow me to get past the first question. Should i just have not tried to chart the contrapositives at all? Should you never chart the contrapositives of conditional sequencing chains? so so confused

Thanks for the help
• PowerScore Staff
• Posts: 5243
• Joined: Apr 14, 2011
#94977
In this case, frk215, doing the contrapositives is a waste of time and effort, because those two rules already split the game into two distinct templates - either H is before G, or G is before H. Doing the contrapositive of the first rule about G and H will just force you into the second rule about them, so you're better off just diagramming those two sequences and then adding in all the other rules, as shown in our explanation where they generate two templates.

That said, I do suggest diagramming contrapositives most of the time, if doing so will help you more clearly see the relationships and inferences. The test makers love to test us on the contrapositives, and love to give us wrong answers based on Mistaken Reversals and Mistaken Negations. Although they don't do any good here, they will often do you a lot of good, so you should at least think about them and in many cases you should draw them out.
romankd
• Posts: 3
• Joined: Sep 23, 2023
#105811
Although I understand the contrapositives are a waste of time because of the next rule. For learning purposes, I am wondering what the contrapositive would be for the second rule
Dana D
• PowerScore Staff
• Posts: 363
• Joined: Feb 06, 2024
#105833
Hey Roman,

I wouldn't call this a contrapositive, but the opposite of this rule would just be that if G is not more expensive than H, the alternative is that H is more expensive than G. If the 3rd rule didn't exist, then we wouldn't have any other information, the additional factor of "neither K nor L being more expensive than J" just doesn't apply.

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