Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is an Advanced Linear: Balanced game.

The game scenario links two variable sets—airlines and planes—together:

PT58-Sept2009_LGE-G3_srd1.png

The remainder of the scenario establishes that each plane flies exactly once. At this point, you cannot be certain of exactly what type of game this is going to be, and so you should expect that the rules will add sufficient information to determine the game type.

Rule #1. This rule establishes that the planes take off in a linear fashion, and as such we can now determine that this is an Advanced Linear game with at least three variable sets: the order of the plane departures, the planes, and the airlines.

Rule #2. This rule adds a new variable set: domestic/international flight status. Thus, at this point, the basic setup of the game appears as follows.

PT58-Sept2009_LGE-G3_srd2.png

The first two rules provide a good example of why you must read each rule prior to beginning your diagram.

Rule #3. This is the first rule to address individual variables. The rule creates a vertical block:

PT58-Sept2009_LGE-G3_srd3.png

Rule #4. This rule creates two more vertical blocks:

PT58-Sept2009_LGE-G3_srd4.png

Rule #5. This rule produces a basic sequence within the domestic/international variable set:

PT58-Sept2009_LGE-G3_srd5.png

Because several planes have already been assigned as D or I flights, this rule can be used to link the blocks created in rules #3 and #4. More on this in the rule #6 discussion. In the meantime, because we know from rules #3 and #4 that at least two D flights and at least one I flight already exist, we can determine that an I flight is first, and the last two flights are both D flights. Not Laws can then be created referencing P, Q, and R, which have all been established as domestic or international flights.

PT58-Sept2009_LGE-G3_srd6.png

Rule #6. This rule establishes another sequence, this time linking the domestic flights and the airlines variable sets:

PT58-Sept2009_LGE-G3_srd7.png

Because this rule addresses both domestic flights, we can link this rule with the fifth rule, which states that any international flight departs before any domestic flight:

PT58-Sept2009_LGE-G3_srd8.png

Given this powerful rule configuration, let’s take a moment to consider the domestic flights for Flyhigh airlines:

P and Q are the only two Flyhigh planes, and the third and fourth rules establish that P is an international flight and that Q is a domestic flight. Thus, Q is the only domestic flight on Flyhigh airlines.

Because all international flights depart before any domestic flight, we inferred that at least the last two flights are domestic flights. Because all Getaway domestic flights depart before Flyhigh’s domestic flight, we can infer that Flyhigh’s Q must be the last flight, and, because there is only one Flyhigh domestic flight, we can infer that the fourth flight must be from Getaway airline:

PT58-Sept2009_LGE-G3_srd9.png

Because Q must be the fifth flight, we can remove the Q Not Law from the first flight, and the P Not Law from the last flight, for the sake of clarity in our diagram. On the test, we would simply leave them there as they cause no harm.

Additionally, while the fourth flight could be R, it does not have to be, and hence no inference can be made involving the fourth flight. All that we can infer is that P R, due to the interaction of the third, fourth, and fifth rules.

The combination of rules and inferences leads to the final setup for the game. In the initial listing of variables, D/I subscripts have been used to note the status of individual planes. Although this information is also displayed elsewhere, listing this information on the variables makes the connections easier to remember.

PT58-Sept2009_LGE-G3_srd10.png

[srcline@noctrl.edu]

Hello

I was completely lost on this game. Would someone please explain the set up of this game, I understood the rules, but the set up is giving me the most problems. In relation to the setup, would the last rule give any clues?

Thankyou
Sarah

[Clay Cooper]

Hi Sarah,

Thanks for your question! I will walk through the thought process as we set up this game and explain how we can know what the setup and diagram should look like (and thus make sense of the game).

The first detail we notice is that the variables (P,Q,R,S, and T) are each drawn from one of two groups: F and G. Though this grouping-like element is the first thing we notice, it quickly becomes apparent as we read on that we are dealing with a sequencing game of some kind, because order matters. We can tell that from the fact that our rules include a no-ties rule (each plane departs one at a time), a rule telling us each plane only departs once, and (especially) from the rules that state that one or more planes must depart before or after one or more other planes; this last piece of evidence in particular suggests that our job will be to determine the sequence of departures. Finally, we can peek ahead to the first question and if (as is very often the case) its answer choices represent possible permutations of the game, what they look like will give us a hint as to what our diagram should look like; in this case, the answer choices are each a permutation – or sequence of all the variables – and it thus becomes clear that the most important part of our diagram will probably be a row of five blanks into which we place the five airplanes.

Our diagram is not yet finished, however; as we read on we notice that some of the rules are expressed in terms of which airline owns a particular plane, and not that plane’s actual name; thus we must add a line of blanks above our original line, in order to allow ourselves to fill in F or G for each of the five planes to track what airline owns it. The same becomes necessary to determine whether each plane flies domestically or internationally (D or I), and what we end up with looks something like this:

_ _ _ _ _ D/I
_ _ _ _ _ F/G
_ _ _ _ _ plane
1 2 3 4 5

Our rules, then, become much easier to handle; they must simply reflect what they will mean for our diagram. For instance, the third rule should look when notated like a vertical block, three rows high, that makes it clear that the column of blanks which has P on its bottom and F in its middle will have I on its top.

I
F
P

From there, our rules will fit together nicely and the questions should not through us for a loop (though they may not be easy).

Thanks again for your question, keep up the hard work!

[srcline@noctrl.edu]

Hello Clay,

This makes so much sense. I thought this was a grouping game because of the two airlines, but I definitely overlooked the rules on this one, especially the first rule. It makes sense why this would be a sequencing given the first and last two rules.
I also understand the set up and now also because rules (last two) indicate order.

Thankyou very much
Sarah

[srcline@noctrl.edu]

Hello,

So I ran into more problems with this game, not sure if I am understanding the set up, how do we know to put

D/I - - - - -

F/G- - - - -

Plane: - - - - -

This doesnt make sense to me.

Thankyou
Sarah

[David Boyle]

Hello,

So I ran into more problems with this game, not sure if I am understanding the set up, how do we know to put

D/I - - - - -

F/G- - - - -

Plane: - - - - -

This doesnt make sense to me.

Thankyou
Sarah

Hello Sarah,

In this Advanced Linear game, you have several "stacks": one for domestic/international, one for Flyhigh/Getaway, and then one for the letters of each plane.

Hope this helps,
David

[emma4832]

I understand the setup of the game, but I'm wondering if someone can walk through the inferences/where to go from here.

I have that P (i/F) must come before R (d/G) which must come before Q (d/F). From there I wasn't sure how many possibilities to identify. I also have that R and Q cannot go first, Q cannot go second, P cannot go fourth or fifth, and R cannot go last.

[Jeremy Press]

Hi Emma,

You've actually made nearly all the inferences I would've made in my initial diagram here, so nice job! The other inferences I would've made right off the bat are that an International flight must be 1st (because there is at least one International flight), and Domestic flights must be 4th and 5th (because there are at least two Domestic flights).

There's a somewhat tricky inference around Q, tested in question 16. Because it's Domestic and Flyhigh, it has to be last. This is because the other Flyhigh flight is International (and therefore has to come before it), and because whether you make the three Getaway flights Domestic or International, those flights will have to come before it. If you didn't see this inference up front, it's not a major setback, because you can still arrive at it once you've done some of the Local questions and seen that it is a consistent element in the game. For example, answer choices C, D, and E in question 16 can be eliminated immediately using the correct answer from question 13.

Below is a screenshot of a proposed diagram. I wouldn't advise using the "Identify Templates" or "Identify Possibilities" approaches, because there are too many uncertainties around placement involving S and T (whether they turn out to be Domestic or International). What you'll want to do is dive in on any Local questions, to get a little clearer picture of how the game plays out in individual situations. Then you can return to the Global questions with enough information to eliminate some answers and arrive as efficiently as possible at the correct answer.

Diagram Sept 2009 Game 3.png

I hope this helps!

Jeremy