Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Defined-Fixed, Unbalanced: Overloaded, Identify the Templates game.


This game is widely regarded as the most difficult game on the October 1999 LSAT. The initial
scenario and the fourth rule establish the basic setup for the game:

The first rule establishes that neither mannequin wears all three colors:

Of course, because mannequin 1 already wears the red tie, the rest of mannequin 1’s outfit will be
red and navy, or red and yellow. More on this later.

The second rule indicates that each individual mannequin wears a different colored hat and jacket:

The third rule indicates that mannequin 2 wears a navy skirt:

A logical starting point for our inference analysis is the skirt of mannequin 1. Because mannequin
2’s skirt is navy (and there is only one navy skirt, so mannequin 1 cannot wear a navy skirt), the skirt
of mannequin 1 must be red or yellow:

This inference, when combined with the first two rules, results in a situation where:

     1. If the skirt of mannequin 1 is yellow, then either the jacket of mannequin 1 is red and the
     hat of mannequin 1 must be yellow, or the jacket of mannequin 1 is yellow and the hat of
     mannequin 1 must be red;

     2. If the skirt of mannequin 1 is red, then the jacket and hat of mannequin 1 is some
     combination of red and yellow or of red and navy.

Because the options for the jacket and hat of mannequin 1 are restricted according to the color of the
skirt of mannequin 1, one approach is to Identify the Templates:

When mannequin 1’s skirt is yellow:

Under both scenarios, the jacket and hat on mannequin 2 are locked into a dual-option, which is
represented by the two blocks and the slash. For example, in Template #1 if the jacket of mannequin 2
is navy, then the hat of mannequin 2 is red.

Of course, mannequin 1’s skirt does not have to be yellow, and could be red instead:

When mannequin 1’s skirt is red:

This second set of templates is very open, but still quite useful. If you feel that those two templates
are insufficient, you could instead show the four basic possibilities when the skirt of Mannequin 1 is
red. We’ll show those possibilities for demonstration purposes:

While we have shown these last four possibilities under Templates #3 and #4, it is not essential that
you do so, because it can be a bit too time-consuming (not to mention that space is limited in this
game because the seven questions take up so much room). The basic template approach is sufficient.

[nghiem505]

I feel like I am missing some key part to this game, since questions 9-13 implies that the two mannequins has some sort of interactions with one another. However, I see no interaction between the two. For example, on question 11, how does what mannequin 2 wears affect what mannequin 1 must wear at all. Please help. I have no answers.

[Nikki Siclunov]

Hi,

Thanks for your question.

The game contains 10 variables:

Hats: N, R, Y
Jackets: N, R, Y
Skirts: N, R, Y
Ties: R

Each mannequin wears exactly one hat, one jacket, and one skirt, but neither wears all three colors. Also, the hat must always be in a different color from the jacket. The rules of the game can be represented as follows:

Mannequin 1:
Hat:
Jacket:
Skirt: RED/YELLOW
Tie: RED

Mannequin 2:
Hat:
Jacket:
Skirt: NAVY

Because mannequin 2 wears the NAVY skirt, mannequin 1 must wear either the RED skirt or the YELLOW skirt. Recall, however, that mannequin 1 already wears a RED tie, and no mannequin can wear all three colors. Consequently, if mannequin 1 were to wear a YELLOW skirt, that mannequin cannot wear any NAVY article of clothing, and so both the hat and the jacket must be RED/YELLOW and YELLOW/RED, respectively. Alternatively, if mannequin 1 wears the RED skirt, then the rest of the outfit (i.e. the hat/jacket combination) must not be NAVY/YELLOW (or else you'll have all three colors in its outfit). So, if mannequin 1 wears the RED skirt, then either its hat, or else its jacket, must be RED.

This observation should enable you to make 2 templates, based on whether mannequin 1 wears the RED skirt or the YELLOW skirt. As far as mannequin 2's outfit is concerned, recall that mannequin 2 already wears the NAVY skirt. No mannequin can wear a hat in the same color as the jacket, and no mannequin can wear all three colors in its outfit. It follows that mannequin 2 must always wear either a NAVY hat, or a NAVY jacket (otherwise, the hat/jacket combination for that mannequin will end up being RED/YELLOW, which - combined with the NAVY skirt - will end up violating the first rule of the game). Combined with the inference in the first paragraph, you should be able to construct powerful templates to attack the questions in this game.

Let me know if this helps.

[srcline@noctrl.edu]

Hello

Are my templates correct Man 1:

Temp 1: Temp 2:
H:R H: Y
J: Y J: R
S: Y S; Y
T: R T: R

I am also having trouble with Man 2's template

Man 2

Temp 1 : Temp 2
H: R H: N
J: N J: R
S: N S: N


Thankyou
Sarah

[Adam Tyson]

Sarah,

Looks like you are going for solutions rather than templates - that is, you are trying to come up with all the variations rather than just guidelines with some variability in them. Also, keep in mind that you can't work out the mannequins in isolation from one another - once you use the red hat, for example, on one mannequin, the other one can't wear that same red hat. Here's what I mean, for just one template:

Man 1: Red Hat, Yellow or Navy Jacket, Red Skirt, Red Tie
Man 2: Yellow or Navy Hat, Red or Navy or Yellow Jacket, Navy Skirt

Notice that this template is very "loose" and that you still have to pay attention to all the rules. You could break this template down into two solutions if you prefer, as follows:

Man 1: Red Hat, Yellow Jacket, Red Skirt, Red Tie
Man 2: Yellow Hat, Navy Jacket, Navy Skirt

Man 1: Red Hat, Yellow or Navy Jacket, Red Skirt, Red Tie
Man 2: Navy Hat, Red or Yellow Jacket, Navy Skirt

This is only the beginning, though, because these are all based on Man 1 wearing the Red Skirt AND the Red Hat. What if that mannequin has the Yellow Skirt, or the Yellow or Navy Hat? The idea behind templates is to capture a broad range of possible outcomes within one framework, with a few things locked in and the rest remaining variable. When you have only two choices (Man 1 wears either the Red Skirt or else the Yellow Skirt, since Man 2 has the Navy Skirt) that is a good situation to try templates based on those two choices. Many things could follow from those two choices, so just identify what MUST happen and then leave some room for flexibility for what COULD happen.

Give that another try and see what happens?

[T.B.Justin]

is this an accurate description of the broad type of game this is: grouping, overfunded-defined, identify the possibilities.

[Charlie Melman]

Justin,

I almost completely agree with you. This is an identify-the-templates game, not an identify-the-possibilities game. The reason is that the game requires us to sketch out multiple general directions in order to find solutions. By contrast, an identify-the-possibilities game requires us to capture every solution during the initial diagramming setup.

[rwraulynaitis]

Would this game be considered a profile charting game?

This game stopped me right in my tracks, and I could not figure out how to diagram it. I ended up using a system of rows and columns in a table-like fashion, but that did not seem the most efficient. Simply writing them out like in the answer above also seemed confusing and jumbled to me .

Do you guys have any guidance on the best way to approach this game?

[Adam Tyson]

Not Profile Charting, rwraulynaitis, just Grouping, with the mannequins as the two groups. Put the Tie in Group 1, and then you need three empty slots for each group, one slot each for hat, jacket, and skirt. From there you are just plugging in the colors!

Try setting up templates, based on which color skirt mannequin 1 wears, either Red or Yellow.