Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is an Advanced Linear: Balanced game.

The linear aspect of this game places three debate teams in order. Each team also has two individual members, and so two spaces are placed above each team for the two members:

PT53-Dec2007_LGE-G4_srd1.png

With three different stacks for the variables, we have an Advanced Linear game. The challenge within this game will be to track the relationship between the different variable sets, and to place the individual members. The placement of the individual members has a strong Grouping element (so much so that this game could easily be classified as a Grouping/Linear Combination game).

Rule #1. This rule combines one variable from the team variable set with one variable from the member variable set. Given our setup above, this rule should be displayed vertically:

PT53-Dec2007_LGE-G4_srd2.png

Note that you could place subscripts (“T” for team and “M” for member) on each variable in order to help with the identification. This choice is purely one of personal preference. We will not use subscripts as there are few enough teams and members to track the two sets without subscripts.

Rule #2. This rule assigns T to the second place team. The best representation of this rule is directly on the diagram:

PT53-Dec2007_LGE-G4_srd3.png

Rule #3. This rule creates a not-block between two members, M and P. The best diagram is a vertical not-block:

PT53-Dec2007_LGE-G4_srd4.png

As with many not-blocks, there is not initial inference produced by the presence of this rule. M and P still have options for each team and placement position. This rule will come into play once other variables are placed, however.

Rule #4. This rule creates a sequential relationship between two team members, in the form of P N. From the sequence, we can determine that N can never be a member of the first-place team, and P can never be a member of the third-place team. These two inferences can be shown as Not Laws under the member stacks:

PT53-Dec2007_LGE-G4_srd5.png

Rule #5. This rule creates a sequential relationship between two teams, in the form of G H. From the sequence, we can determine that H can never be the first-place team, and G can never be the third-place team. These two inferences can be shown as Not Laws under the team stack. Of course, because there are only three teams available for each slot, when one team is removed from the running then only two teams remain, creating a dual-option. Thus, either F or G must be the first-place team, and either F or H must be the third-place team:

PT53-Dec2007_LGE-G4_srd6.png

This rule creates only three possible orders for the three teams: F-G-H, G-F-H, or G-H-F. One option here would be to create three separate templates and explore the options for each. However, we will not pursue this option because, aside from the F-G-H template, the number of different placement options for the members would still be significant.

One aspect of this rule that must be explored is that it contains G, which also appears in the first rule. Because the final rule eliminates G from being the third-place team, connecting that inference to the first rule yields the insight that S can never be a member of the third-place team. This inference can also be shown as a Not Law under the third-place team member spaces.

With S now eliminated from the third-place team, and T (second rule) and P (fourth rule) previously eliminated, only three members are possible candidates for the third-place team: M, N, and O. Thus, if any one of those three members is on a different team, then the remaining two members must be on the third-place team.

Combining all of the above information leads to the final setup for this game:

PT53-Dec2007_LGE-G4_srd7.png

[Jkjones3789]

Hello, I was having some difficulty with this game. I see that it is sequencing and grouping. My diagram looks horrible making it more difficult to solve.How would you go about diagramming this and solving. Would you suggest making templates based on the limited placement of P and N and G and H? Thank you.

[David Boyle]

Hello, I was having some difficulty with this game. I see that it is sequencing and grouping. My diagram looks horrible making it more difficult to solve.How would you go about diagramming this and solving. Would you suggest making templates based on the limited placement of P and N and G and H? Thank you.

Dear Jkjones 3789:

slash (mp)
p > n
s ---> g
g > h

People (mnopst)

Teams (fgh)

---- ---- ----
1 2 3
slash h slash g
slash n slash s
slash p

(The computer is messing up the graphics above: what I'm trying to say is that h and n aren't allowed in spot 1, and g, s, and p aren't allowed in spot 3.)

One could try templates, perhaps.
Say, since g can't be last, the only possibilities may be,

ghf
gfh
fgh

. So, with fgh, it looks like the only possible placement is

psn
otm

. For the others: for gfh, or maybe also for ghf,

s t -
p - -

, with m, n, and o floating around in the free spaces, if you put p in first place with s. If p is in second place, then

s t -
- p n

, with m and o floating around in the free spaces. That all certainly seems to narrow the possibilities.

Hope this helps,
David

[Dajpol]

Can someone revisit this setup and re-diagram? The response by Powerscore encountered formatting issues and thus it's pretty difficult to visualize. If it can't be done, no problem.

Thanks!

[Emily Haney-Caron]

Hi Dajpol,

Happy to review the diagram! Thanks for asking - sometimes the formatting makes things super confusing.

I'm attaching a photo of my written-by-hand diagram, in the hopes that will be easier to read. Basically, the text from David's post is hopefully still useful, but this will give you an idea of what it might look like. The photo is super hard to read in this message, but if you right click and open it in a new window, hopefully you'll be able to see it. Let me know if you have other questions once you look this over!

Emily

IMG_2795.JPG

[Dajpol]

Perfect. Thank you

[srcline@noctrl.edu]

hello

So I'm still a bit confused on this game I set it up as:

1st place:_ _
2ndplace:_ _
3rdplace:_ _

rules:

1. s Gteam
2. T is second place
3. MP (not block)
4. P>N
5. G>H

Inferences:
1. N cant be in 1st place
2. s and P cant be third.
3. O is random

I cant figure out how to determine what people are FGH

Thankyou
Sarah

[Adam Tyson]

Thanks for the question, Sarah. Who is on which team will vary depending on which team places where. In other words, the blocks aren't fixed, with S and T always together on team G, for example. Let's try a few possible solutions and see what happens, shall we?

If the order of the teams if F-G-H (F first, G second, and H third), we know that T and S are on team G in second place (because S is always on team G and T is always in second place). What does that do to our other members? Well, P places higher than N, so P is in first place on Team F and N is in third place on Team H. Since M and P are not on the same team, the only place left for M is on team H in third place, and our random friend, O, joins P on Team F in first place. The solution looks like this:

P T N
O S M
F G H
1 2 3

Now, what happens if the order is something else? Let's say it's G-H-F:

S is on Team G, in first place. T is on Team H, in second place. What else do we know? Much less!

P is on one of the first two teams in order to place ahead of N, but P could be on either of them. If P is second, N is third, and then M and O fill the other two places in either order. If P is first, N could be in either second or thid, and again M and O are interchangeable in the remaining two spaces. Lots of flexibility!

Finally, try a G-F-H order and see what options there are. You'll find it looks a lot like the previous, highly flexible template.

There's not just one solution to this game, and not even just one solution to the teams within the game. It's that variability that makes the game interesting and that gives the test authors so much stuff to work you over with.

Take a look at q19, for example. If P is on Team H, what do we know? H can never be first, and P can never be last, so Team H must be in 2nd place, and T is the other member of that team! G has to place ahead of H, making S and G go to first place. P places ahead of N, so N is in third place, and that's forced to be Team F. Where do M and O go? Once again we find that they are interchangeable, with one of them in first place on Team G with S, the other being in third place on Team F with N. It's a Could Be True question, which tend to focus on the unknown elements, so it's no surprise that the answer is A, about member O.

I hope that helps some! Good luck!

[AJH]

I really struggled with the set up and inferences (and thus the questions!) with this game. Is the best way to draw out the three possible school rankings and see where the team members all fit into each and then use those to answer the questions? I felt like I couldn't diagram it well enough, or make enough inferences to be able to answer questions. This game is a grouping/linear combo, correct?

[nicholaspavic]

Hi AJH,

The rankings make this a Linear Game, the student and schools make the multistacks. So I would characterize this as an Grouping/Linear Game which is balanced with all students and school slots filled, obviously.

There is definitely a valid approach to this game in doing templates using the last two rules to split the game board into 4 separate templates with P - N shifting up and down the 1st through 3rd rank on three possible solutions with the last rule creating the situation where school Gillam and student Sethna go together to either first or second in the ranking to create a 3rd and 4th game template. There are 6 questions to this game after all, so it may be worth the time investment to do the templates and see all the possibilities, especially with the high number of Could Be True questions for this game.

Thanks for the great question and I hope this helps!