Setup and Rule Diagrams

[Administrator]

Setup and Rule Diagram Explanation

This is a Grouping/Linear Combination game.

Full Setup:

D05_Game_#4_setup_diagram_full_a.png

D05_Game_#4_setup_diagram_full_b.png

This is an extremely challenging game, with a unique game setup and a disparate set of rules. The two stages and the performance times should be shown in an Advanced Linear format, with separate rows for each stage. The unavailable times for each stage should be shown with an X in those spaces. Here is the base diagram, with the first rule represented:

D05_Game_#4_setup_diagram_1.png

The remaining rules require further analysis.

Rule #2:

This rule establishes that G performs before H, which can be represented as:

GF > HF

The immediate consequence of this rule is that H cannot perform on the north stage at 6, and G cannot perform on the south stage at 12. These two inferences can be shown as Not Laws on the diagram.

This rule ultimately plays a powerful role in the game, but only in conjunction with other rules.

Rule #3:

This rule indicates that if any rock group performs at 10, then no folk group performs at 10. Thus, if a rock group performs at 10, the other group playing at 10 must also be a rock band. By the contrapositive, if a folk band plays at 10, then the other band playing must be a folk band. This rule, then, leads to two blocks:

D05_Game_#4_setup_diagram_2.png

Thus, the two 10 slots must be performed by bands of the same type.

Rule #4:

According to this rule, L and T must perform on different stages:

D05_Game_#4_setup_diagram_3.png

The rule does not generate a simple not-block; instead the rule applies to each entire stage and the order of the variables is not important (and thus a TL not-block would also be valid, but unnecessary because of the “Stage” subscript on the block). The operating effect of this rule is that L and T cannot perform on the same stage, and thus exactly one of L or T is always performing on the north stage, and the other performs on the south stage.

Rule #5:

This rule also creates a horizontal block, but not one tied to a particular stage. If Q must follow a folk band playing in the prior time slot, the best representation is:

D05_Game_#4_setup_diagram_4.png

Like other rules, this one has a degree of uncertainty to it because Q and the folk band prior to Q can perform on the same stage, or on different stages.

Because this is a fixed block (e.g. the two variables are fixed in consecutive order), Q can never perform in the 6 slot on the north stage, creating another Not Law. There are further implications to this rule as well, such as that if P plays at 6, Q cannot play at 8 (and, via the contrapositive, if Q plays at 8, P cannot play at 6 and must play at 12).

Because of the unusual nature of the rules, there are more inferences in this game, but let’s use the questions to discuss those inferences, and then at the end we’ll provide the complete setup again.

[sarae]

I was just wondering what the best approach to this game is. Would it be best to make templates?

Also, I'm having trouble understanding why question 21 cannot be E. We know that when anything other than P performs at 12, then P must perform at 6. My hypothetical for question E was the following, respectively:
North: P,T,L
South: G, H, Q

Additionally, I don't see the connection that resulted in the answer to question number 22. When it says "a folk group performs at 8," does that mean at 8 on the north and south side?

I'm clearly misunderstanding an important aspect of the game but I can't put my finger on it!

Thanks!

[Lucas Moreau]

First: I would recommend the use of templates for this game. After you have the basic setup, decide which variable would be best to derive templates from. For instance, you could have two templates, one where only rock groups play at 10 and one where only folk groups play at 10. Or you could use the placement of Q as a template, since there would be only three possibilities there, time-wise.

Second: You cannot have PTL on the north stage, as Rule 4 states that L and T must be on different stages.

Third: If a rock group performs at 10, then two rock groups must perform at 10, as per Rule 3. Since P must perform at 6 or 12, this would mean that Q and T both perform at 10, leaving only folk groups to perform at 8. There is no way for a rock group to perform at 10 and no folk group to perform at 8; therefore, B must be true.

Hope this helps,
Lucas Moreau
PowerScore

[sarae]

Oh ok that helps a lot!

For the fourth rule I accidentally wrote the wrong variables!

Thank you!

[T.B.Justin]

I diagrammed this using N and S as the vertical base and staggered to align the time of each performance; curious if anyone did it differently.

[Dave Killoran]

I diagrammed this using N and S as the vertical base and staggered to align the time of each performance; curious if anyone did it differently.

Technically it doesn't matter which one you use as the base as long as you adjust your diagrams appropriately, so you are all good there. I personally would tend to put North and South on the side since I can put North "above" south, as it would happen on a map, but that's not really that big of a deal

Thanks!

[T.B.Justin]

So,
N _ _ _
S _ _ _

?

[Dave Killoran]

So,
N _ _ _
S _ _ _

?

Yes!

But if it's done the following way it works equally well:

• ____ ____
    N      S

Thanks!

[LSAT2018]

Third: If a rock group performs at 10, then two rock groups must perform at 10, as per Rule 3. Since P must perform at 6 or 12, this would mean that Q and T both perform at 10, leaving only folk groups to perform at 8. There is no way for a rock group to perform at 10 and no folk group to perform at 8; therefore, B must be true.

Rock (10) → No Folk (10)
Folk (10) → No Rock (10)

I was just wondering if the third rule can be diagrammed like this, with the contrapositive? It shows a double not arrow for Folk and Rock. But I was wondering if the fact that this refers to both rock groups and both folk groups affect the relationship?

[T.B.Justin]

First: I would recommend the use of templates for this game. After you have the basic setup, decide which variable would be best to derive templates from. For instance, you could have two templates, one where only rock groups play at 10 and one where only folk groups play at 10. Or you could use the placement of Q as a template, since there would be only three possibilities there, time-wise.

I identified 8 possibilities: Q at South 8; 2 with Q at South 10; 2 with Q at South 12; and Q at North 8; 2 with Q at North 10.

How did you break them down into 3 templates?