Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

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

This is a very challenging game. The first indication of difficulty is the Subdivided selection pool—the researchers are either anthropologists or linguists. The second source of difficulty is that there are six researchers selected, but seven available researchers, leading to an Unbalanced scenario. Finally, the fact that each team includes at least one anthropologist and at least one linguist further adds to the information you must track.

The initial scenario appears as follows:

O97_Game_#3_setup_diagram 1.png

Thus, each team includes either one or two anthropologists and either one or two linguists.

The first two rules establish negative grouping rules, which will be shown as vertical not-blocks:

O97_Game_#3_setup_diagram 2.png

The third rule establishes two more negative grouping rules:

O97_Game_#3_setup_diagram 3.png

Because M appears in both blocks, the researchers that can be included with M are limited. Because M is an anthropologist, and each team must have an anthropologist and a linguist, if M is included on a team, then N or O must also be included the same team (because R and S are unavailable):

• M N/O

The final rule is conditional:

• J1 R2

Because R appears in two of the other rules, take a moment to consider the implications of this rule. When J is included on team 1, then R must be included on team 2. But, because R cannot be included on a team with M, and each team must have at least one anthropologist, if J is included on team 1, then R and F (the only remaining anthropologist) must be included on team 2:

• [J1 R2] F2

Via the same reasoning, if R is included on team 1 (and from the rules then J and M cannot be the anthropologists on team 1), then F must also be included on team 1.

• R1 F1

The information derived so far can be added together to create the final diagram:

O97_Game_#3_setup_diagram 4.png

[stephenaspro]

Hi,

This game took me quiet some time and I am thinking it is because of my setup.

I wrote out the 2 variable groups as:
A: FJM 3
L: NORS 4
And then I wrote out the rules:

Below I had the board with group 1 and group 2 with 3 spaces each and one space off to the side to remind myself that somebody would have to be out. I couldn't think of any inferences to add so I moved on to the questions. Are there key inferences to this game that I missed?

[AthenaDalton]

Hi Stephen,

Your approach sounds spot-on. There are too many possible diagrams in this game to sketch out possibilities up front. Once you have a clear understanding of the rules, it's best just to jump into the questions for this game.

In open-ended games like this one, many questions will provide an additional rule which you can then use to sketch out diagrams.

Good luck studying!

Athena Dalton

[LSAT2018]

Given the last rule, 'If team 1 includes Jones, team 2 includes Rice' I was wondering about the implications of the contrapositive.

Since there are six researchers to be chosen out of a group of seven researchers, the two-group system (contrapositive indicates if Rice is in team 1, then Jones would be in team 2) would not work?
So the contrapositive is if Rice is in team 1 (or out), then Jones would be in team 2 (or out). And so because of the uncertainty, the contrapositive is not very useful in this game.

[Adam Tyson]

I wouldn't say it isn't useful, LSAT2018. Quite the contrary, the contrapositive is almost always worth considering and frequently leads to answering a question in the game. But keep the contrapositive simple and clear here: If R is NOT in Team 2, then J is NOT in Team 1. You have the implications correct (if R is either in Team 1 or out, then J is either in Team 2 or is out), but start with just the contrapositive as it is, using the negations.

How might that play out? Consider what happens when R is the researcher not selected. Then J could not be on Team 1, and he also could not be out, because R is the only one that's out (we have to select 6 of the 7 researchers to fill the two teams, so each solution has just one researcher not selected). That means J would have to be on Team 2! Pretty useful inference, potentially!

When you have a two-value system, with only two options for each variable the contrapositives can be expressed more powerfully by saying where a variable is instead of where it is not. If, for example, the game had all 7 variables placed on the teams, then if we knew that R was not on Team 2 it would have to be on Team 1, and instead of saying "R is not on Team 2" we would express it in the positive form, "R is on Team 1". But just because this is not a two-value systems like that doesn't mean we can't use the contrapositive. Always be aware of it and consider its ramifications, even if you decide not to diagram it in your setup.

[ava17]

Is it true to make the inference that if S is in a team, J must be on that team? Because S can not be with F or M, but each team needs at least one anthropologist? I didn't see this tested in the questions, so want to make sure that inference was correct (if unnecessary). Thanks!

[Jay Donnell]

Good spot, Ava17!

As you correctly deduced, since each team needs at least one anthropologist, the inclusion of S to a team would rule out both F and M, and therefore require J to join the team.

Great work!

In the classic words of the narrator to my favorite childhood tv show, Where in the World is Carmen San Diego, "good going, gumshoe!"

[gwlsathelp]

Hi, I am having a hard time understanding the third rule, which ended up being crucial to understanding the game. The phrasing on this is hard for me to understand: "if a team includes Marquez, it includes neither Rice nor Samuels".

My interpretation:
M RS
where you could either have MS or MR as a pairing/block but not RS.

Powerscore interpretation:
M MS or MR
where RS could be a pairing but neither MR nor MS could be used as a pairing/block.

What is it in the phrasing that indicates this?

[Adam Tyson]

The use of "neither this nor that" means "not this AND not that, " gwlsathelp. Your interpretation would be correct if the rule had said "If a team includes Marquez, it cannot include both Rice nor Samuels." But "it includes neither Rice nor Samuels" means they must both be excluded from any group that includes M.

If I say "I will have neither steak nor chicken for dinner," I'm not saying I might have steak or chicken but not both. I'm saying I won't have either one. The same principle applies to this rule, and to any others you see like it.

Remember that rule: "neither...nor" means "not this AND not that." Both must be out!

[pwfquestions]

Could you draw the first few rules as not arrow laws like F<l>S ?