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Setup and Rule Diagrams

LSAT Apprentice
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I am having trouble setting up this game, making nferences etc.
Could someone please explain how to set this game up and make the inferences?
Francis O'Rourke
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This is a Defined, Overloaded, In & out grouping game.

We have to select 5 out of 9 scientists, so we need 5 scientists in the "IN" group and 4 scientists in the "OUT" group.

What makes this game a bit harder is that the 9 scientists are split into three groups of three scientists, which yields the following set of variables:

Botanists: FGH
Chemists: KLM
Zoologists: PQR

Here's one way to set up the Diagram:

Bot: ____ ____
Che: ____ ____
Zoo: ____ ____
.....IN OUT

The first rule tells us that we must have at least one of each type of scientist on the team, so there are two options for the possibile numbers of each scientist types. Either 3 of one kind and 1 each of the other two, or 2 of two kinds and 1 of the third kind: i.e 3,1,1, or 2,2,1

The second rule states that if we have two or more Botanists, there is only one Zoologist selected. This one is hard to diagram, but what it really tells us is that when you see two Botanists, you cannot have two Zoologists and vice-versa. you could diagram it this way:
2Bot :dblline: 2Zoo

Thus, if the arrangement of types of variables is 2,2,1 then we have to select 2 Chemists

The third and fourth rules tell us the following
F :dblline: K
M :dblline: K

And the final rules tells us
M :arrow: P
M :arrow: R

There are not many inferences that you can get from these rules, but I saw one thing that happens when M is selected. Putting the rules together, we can see that if M is selected then we must also select P and R and K must not be selected:
M :arrow: P & R, K

Which looks like this on the diagram:
Bot: .....___ ..... ____
Che: ..... M ..... K
Zoo: .....PR ..... ____
..........IN ..... OUT

Since there are two Zoologists whenever M is selected, we can only have 1 Botanist, so we can also infer that when M is selected only one Botanist will be selected, and either Q or L will be selected to make 5 total scientists for the panel.

There's not much on this game to do before you get to the questions, but let me know if you have any other questions so far!
LSAT Apprentice
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Hi PS!

Could you please explain how you set up the game. Not quite understanding the in/out portion since we are must have 5 in and 4 out.

Adam Tyson
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We chose to set up the IN group using three sub-groups based on the types of scientists, because we need at least one of each sub-category. That's why you see three slots for IN and three for OUT, to represent the three types. There can be multiple scientists from one type in each group, though, and we handled that with the numeric distrubtions.

Another approach is to make 5 slots in the IN group and 4 in the OUT group, and then label some of the IN slots as being for each type of scientist, something like this:

B __
C __
Z __
? __
? __


Your OUT group could be just four empty, unlabeled slots, or you could label some of them if you make inferences about which ones must be out. For example, if you know for sure that at least one Chemist is always out, you could label one of the slots in the OUT group with a C.

I hope that clarifies it for you! If not, show us how you would propose to do it, or where this approach is going badly for you, and we will happily compare notes.
Adam M. Tyson
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Edit: change underfunded to overloaded, thanks Adam!

I identified this game as Grouping: Unbalanced-overloaded, unfixed-numerical distribution

I worked out 4 templates each in the 3-1-1 distribution and 2-2-1 distribution- did anyone identify more?

I also found that in the 2-2-1 distributions:

When G or H is the only botanist selected and M (chemist) is selected, Q cannot be selected.
Last edited by T.B.Justin on Tue Jan 15, 2019 7:26 am, edited 1 time in total.
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Does the F :dblline: K mean that one of F and K must be in the out group?
Adam Tyson
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That's exactly right, ava17! The same goes for K and M - at least one of them must always be out. That's a good way to read the double-not arrows: "at least one of these two variables is out, maybe both are." We also often discuss it in terms of what is in, saying "these cannot both be in." Both are correct statements, just looking at the relationship from two different angles. Well done!

And TB, you're almost right on the game type. It's actually overloaded, not underfunded, because there are more variables (9) than can be selected to fill the spaces (5). An underfunded game would be where there are not enough variables to fill the slots, such that either some variable must repeat or else some slots go unfilled. There are only the two numeric distributions. Not sure I would pursue templates on this one, and I am a bit of a template junkie. If there are more than 4, then it's probably not even worth chasing them down, especially since there are only 5 questions.
Adam M. Tyson
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