Setup and Rule Diagrams

[Administrator]

Setup and Rule Diagram Explanation

This is an Advanced Linear Game: Unbalanced: Underfunded.

The five-year period forms a natural base for this game, and the car purchases and graduations should be stacked on top of the base. The remaining variable set—the three friends—should be used to fill in the spaces in the car and graduation rows, as such:

Sept 06_game #3_M12_L4_explanations_game#3_setup_diagram_1.png

The friends variable provides uncertainty in this game, namely because the number of variables is fewer than the available slots. At first, it appears that the three friends will fill three spaces in each row (the graduation row and the car row), leaving two empty space variables (E’s) to fill the two remaining slots in each row. If this was the case, the Underfunded aspect of the game would be easily deflected. But, the second-to-last rule makes it clear that R and S will graduate in the same year, meaning that there are three E’s in the graduation row (along with an RS block and variable S). In the car row there are 2 or 3 E’s, depending on when R buys his car (R could conceivably buy a car in the same year as S or T). Let’s look at each rule, with the exception of the last rule, which can be represented right on the diagram (subscripts are used to represent the car/graduation elements):

Sept 06_game #3_M12_L4_explanations_game#3_setup_diagram_2.png

These four rules can be combined into one super-sequence:

Sept 06_game #3_M12_L4_explanations_game#3_setup_diagram_3.png

This sequence is immensely powerful in this game because it limits the placement of a number of variables. In fact, the sequence is so powerful that there are only two possibilities for the graduation row. However, other than mentioning this fact, we tend not to diagram out those options because the sequence is so strong that we do not need to expend the time diagramming out the options. Let us instead look at the complete diagram to the game, adding in Not Laws and the dual options created by the super-sequence:

Sept 06_game #3_M12_L4_explanations_game#3_setup_diagram_4.png

From the sequence, the graduations of the three friends must be after Sue bought her car but before Taylor bought his car, and thus 1991 and 1995 in the graduation row must be empty (E). In addition, because three separate yearly events occur after S bought her car, Sue can only have bought her car in 1991 or 1992 (and this is represented by a dual-option). Similarly, because three separate yearly events occur before T bought his car, Taylor can only have bought his car in 1994 or 1995 (represented by another dual-option).

Note that the last rule, which states that “at least one of the friends graduated in 1993,” is represented by an E Not Law under 1993 in the graduation row.


UPDATE per some discussion below: this is a game that can definitely be attacked/solved with two Templates (based on the gradation options—RS or T—in 1993), so if you approached it with that strategy you're totally in the clear!

Here's what they look like:

Template 1 (RS graduate in 1993):

Car:    _S/_ _/S_ ____ ____ _T__ Rc?
Grad: ____ ____ _RS_ _T__ ____
               1       2       3       4       5

Template 2 (T graduates in 1993):

Car:    _S__ ____ ____ _T/_ _/T_ Rc?
Grad: ____ _RS_ _T__ ____ ____
               1       2       3       4       5


Hope this helps!

[LSAT2018]

For underfunded games, are the empty slots always placed? Or is there some kind of specific situation in which empty slots are needed?

Are there any examples of other games that make use of empty slots?

[Adam Tyson]

I hesitate to say that anything is always true about the LSAT, because there seems to be an exception to every one of those supposed rules. That said, in most underfunded games, it makes sense to include the spaces that might be left empty, if that is a possibility. Being underfunded doesn't automatically mean there will be empty spaces though. For example, look at the second game from December 2008, where 4 people move three pieces of furniture, each piece being moved by two people. That's 4 variables into 6 slots, a classic underfunded game, but none of the spots will be empty. Instead, one or more variables will have to repeat in order to fill the extra spaces.

Compare that to, for example, the third game in December 1996, where we have six days to interview witnesses, and the interviews take place in the mornings and afternoons. There are 6 witnesses that each fill one entire morning or else one entire afternoon, not both, and then two whole consecutive days for some additional unknown number of Hostile witnesses that are not part of that group of 6. There are 12 potential time slots - 6 days, morning and afternoon for each day - but only 10 of them will be filled (four by a block of hostile witnesses, 6 by the ones listed as non-hostile). That leaves two empty slots. Would we include those in the setup? Absoutely! That's part of our base, and we wouldn't know which ones to exclude if we tried.

In general, if there are fewer variables than there are spaces in which to places them, you should have empty spaces in your diagram, or else you can create a new variable as a placeholder to represent that the space is empty (we usually use an X for that purpose, unless X is one of the variables in the game). The base is there to receive the variables per the global and local rules and inferences, and if a space doesn't end up receiving anything, so be it. You'll probably get a question or two about those empty spaces, so it's good to have them in your diagram.

[Adam Tyson]

For contrast, check out this game from October 2008:

lsat/viewforum.php?f=165

One could view this as an underfunded game, in that there are 3 associates sending messages but anywhere from 4 to 6 messages being sent. Here, we would NOT set up empty spaces, with a row of six potential messages that may stop short at 5 or 4. Instead, we would handle this game with templates based on the three numeric possibilities of 4, 5, or 6 messages.

I don't think many of us would have called this game "underfunded," but it is in the sense that the number of variables is lower than the minimum number of spaces, so I think it's fair to say this is an exception to that general rule. So, not always, but usually.

[lsatbossintraining]

Hi Adam and team -

Took a stab and creating two layers with this game and it was a complete mess! Really didn't get anywhere and spent nearly 5 minutes setting up.

7Sage YouTube sets this game up using one layer with subscripts. Found that approach much better frankly: Created two templates and the rest was smooth sailing.

Why doesn't PowerScore set this up in the same way? Is there a reason why two layers is the preferred approach over here?

Finally, how do I know when to stick to one layer even though I'm tracking more than one variable set, as in this game? Any directions to similar games for practice would be much appreciated.

Many thanks,
Kyle

[KelseyWoods]

Hi Kyle!

With this game, we luck out because almost all of the variables (except for Rc) are included in one super sequencing chain and there are several empty slots. This makes it fairly easy to set up in a single layer. In other similar games, however, you might not have as much sequencing information or you might have fewer empty slots, which would make it trickier to keep in a single layer. So basically, double layers will always work in a game like this, single layers work well sometimes, but not so well other times, depending on the types of rules you get. So for the sake of consistency (and so that you don't have the added task of having to figure out when to do a single layer vs a double layer), we stick to double layers. Basically, it's best to stick to consistent ways of diagramming games because while there may be a super cool way to diagram one individual game, if you can't apply those diagramming techniques to other games, it's not going to help you out very much with the totally new games you'll encounter on test day.

I think what really helps out with this game is not so much keeping it to a single layer, but using templates. As you said, you can create 2 templates for this game based on who graduates in 1993. That's easy enough to do with 2 layers:

Template 1 (RS graduate in 1993):

Car:    _S/_ _/S_ ____ ____ _T__ Rc?
Grad: ____ ____ _RS_ _T__ ____
               1       2       3       4       5

Template 2 (T graduates in 1993):

Car:    _S__ ____ ____ _T/_ _/T_ Rc?
Grad: ____ _RS_ _T__ ____ ____
               1       2       3       4       5


Hope this helps!

Best,
Kelsey

[lsatbossintraining]

Much appreciated, Kelsey. Guess the not-laws in the above explanation threw me off. Trying to unlock those inferences with all those not-laws was difficult and definitely a time-suck. Will give this game another shot using two layers to see if I have better luck.

Kyle

[SwanQueen]

Setup and Rule Diagram Explanation

This is an Advanced Linear Game: Unbalanced: Underfunded.

The five-year period forms a natural base for this game, and the car purchases and graduations should be stacked on top of the base. The remaining variable set—the three friends—should be used to fill in the spaces in the car and graduation rows, as such:

Sept 06_game #3_M12_L4_explanations_game#3_setup_diagram_1.png

The friends variable provides uncertainty in this game, namely because the number of variables is fewer than the available slots. At first, it appears that the three friends will fill three spaces in each row (the graduation row and the car row), leaving two empty space variables (E’s) to fill the two remaining slots in each row. If this was the case, the Underfunded aspect of the game would be easily deflected. But, the second-to-last rule makes it clear that R and S will graduate in the same year, meaning that there are three E’s in the graduation row (along with an RS block and variable S). In the car row there are 2 or 3 E’s, depending on when R buys his car (R could conceivably buy a car in the same year as S or T). Let’s look at each rule, with the exception of the last rule, which can be represented right on the diagram (subscripts are used to represent the car/graduation elements):

Sept 06_game #3_M12_L4_explanations_game#3_setup_diagram_2.png

These four rules can be combined into one super-sequence:

Sept 06_game #3_M12_L4_explanations_game#3_setup_diagram_3.png

This sequence is immensely powerful in this game because it limits the placement of a number of variables. In fact, the sequence is so powerful that there are only two possibilities for the graduation row. However, other than mentioning this fact, we tend not to diagram out those options because the sequence is so strong that we do not need to expend the time diagramming out the options. Let us instead look at the complete diagram to the game, adding in Not Laws and the dual options created by the super-sequence:

Sept 06_game #3_M12_L4_explanations_game#3_setup_diagram_4.png

From the sequence, the graduations of the three friends must be after Sue bought her car but before Taylor bought his car, and thus 1991 and 1995 in the graduation row must be empty (E). In addition, because three separate yearly events occur after S bought her car, Sue can only have bought her car in 1991 or 1992 (and this is represented by a dual-option). Similarly, because three separate yearly events occur before T bought his car, Taylor can only have bought his car in 1994 or 1995 (represented by another dual-option).

Note that the last rule, which states that “at least one of the friends graduated in 1993,” is represented by an E Not Law under 1993 in the graduation row.


UPDATE per some discussion below: this is a game that can definitely be attacked/solved with two Templates (based on the gradation options—RS or T—in 1993), so if you approached it with that strategy you're totally in the clear!

Here's what they look like:

Template 1 (RS graduate in 1993):

Car:    _S/_ _/S_ ____ ____ _T__ Rc?
Grad: ____ ____ _RS_ _T__ ____
               1       2       3       4       5

Template 2 (T graduates in 1993):

Car:    _S__ ____ ____ _T/_ _/T_ Rc?
Grad: ____ _RS_ _T__ ____ ____
               1       2       3       4       5


Hope this helps!

I was wondering, why is it impossible for R+S to graduate in 93', and T in 95?
The two templates do not display this option, yet I do not see any rule that prohibits this from happening.

Thanks in advance!

[Robert Carroll]

Swan,

The second rule would prevent that. T must graduate in some year before the year in which he bought his first car, so he cannot graduate in 1995, as that would force his first car purchase off the chart.

Robert Carroll