#21 - Local, Must Be True

[Administrator]

Please post below with any questions!

[lunalondon]

Hello Powerscore,

For this question I diagrammed two different possibilities:

1) R: K2/M2/O2 & L2
S: F1 & Y3 & Z3
T: G1

2) R: K2 & M2 & O2
S: L2 & F1
T: Y3 & Z3 & G1

In both cases I get that Trustcorp owns a class 1 building (answer choice A) but in both cases I also get Southco owning the Flores Tower (answer choice E). Am I missing something? Thank you!

[Jonathan Evans]

Hi, Luna,

Good question. Key point here is to focus not on the buildings themselves but on their classes.

Starting assignment:

• R: G(1) Y(3) Z(3)
  
  S: F(1) L (2)
  
  T: K(2) M(2) O(2)

Now consider the question. It asks what must be true after "some" unspecified number of trades. Thus, we should start with the broad parameters. In this case, we want R to have all class 2 buildings. R has one class 1, worth two class 2s, and two class 3s, worth one class 2.

Break it down by these broad outlines, starting with the condition that R have all class 2:

• R: (2) (2) (2)
  
  S:
  
  T:

The class 1 must have been traded for two class 2, so we know that R got two class 2s from T:

• R: (2) (2) (2)
  
  S:
  
  T: (1)

The two class 3s could have gone to either S or T, but regardless S still has a class 1. The location of the other class 2 and two class 3s is not determined:

• R: (2) (2) (2)
  
  S: (1) [(2) OR (3) (3)]
  
  T: (1) [(3) (3) OR (2)]

Since we're looking for what must be true, let's just start with the baseline fact that T has to have a class 1 building, so we're done.

But now with respect to answer choice (E), note that either S or T could end up with the class 1 building F. Remember, we're given an unspecified number of trades, so T and S could swap F and G to their hearts' content.

The bigger point here for games is to start by considering the defining qualities of items in multidimensional games. Then work inward towards specifics.

[lunalondon]

Thank you!

[quan-tang@hotmail.com]

what confused me was the 'after some number of trades' . I am not certain if after some defined number of trades, it is impossible for them to trade things around enough that none can be inferred about the starting composition.

Hi, Luna,

Good question. Key point here is to focus not on the buildings themselves but on their classes.

Starting assignment:

• R: G(1) Y(3) Z(3)
  
  S: F(1) L (2)
  
  T: K(2) M(2) O(2)

Now consider the question. It asks what must be true after "some" unspecified number of trades. Thus, we should start with the broad parameters. In this case, we want R to have all class 2 buildings. R has one class 1, worth two class 2s, and two class 3s, worth one class 2.

Break it down by these broad outlines, starting with the condition that R have all class 2:

• R: (2) (2) (2)
  
  S:
  
  T:

The class 1 must have been traded for two class 2, so we know that R got two class 2s from T:

• R: (2) (2) (2)
  
  S:
  
  T: (1)

The two class 3s could have gone to either S or T, but regardless S still has a class 1. The location of the other class 2 and two class 3s is not determined:

• R: (2) (2) (2)
  
  S: (1) [(2) OR (3) (3)]
  
  T: (1) [(3) (3) OR (2)]

Since we're looking for what must be true, let's just start with the baseline fact that T has to have a class 1 building, so we're done.

But now with respect to answer choice (E), note that either S or T could end up with the class 1 building F. Remember, we're given an unspecified number of trades, so T and S could swap F and G to their hearts' content.

The bigger point here for games is to start by considering the defining qualities of items in multidimensional games. Then work inward towards specifics.

[quan-tang@hotmail.com]

sorry my brain stuck in the previous reply.

What I meant was, since it says 'after some number of trades', it is not defined how many trades happened, it could be 2000 trades happened or 20,000,000 trades, so can we really infer than two class 2 bulding came from t? could it not possible that in some previous trade, s traded a 2 with t, then the 2 2 class buldings form t would contain one originally from s?

Hi, Luna,

Good question. Key point here is to focus not on the buildings themselves but on their classes.

Starting assignment:

• R: G(1) Y(3) Z(3)
  
  S: F(1) L (2)
  
  T: K(2) M(2) O(2)

Now consider the question. It asks what must be true after "some" unspecified number of trades. Thus, we should start with the broad parameters. In this case, we want R to have all class 2 buildings. R has one class 1, worth two class 2s, and two class 3s, worth one class 2.

Break it down by these broad outlines, starting with the condition that R have all class 2:

• R: (2) (2) (2)
  
  S:
  
  T:

The class 1 must have been traded for two class 2, so we know that R got two class 2s from T:

• R: (2) (2) (2)
  
  S:
  
  T: (1)

The two class 3s could have gone to either S or T, but regardless S still has a class 1. The location of the other class 2 and two class 3s is not determined:

• R: (2) (2) (2)
  
  S: (1) [(2) OR (3) (3)]
  
  T: (1) [(3) (3) OR (2)]

Since we're looking for what must be true, let's just start with the baseline fact that T has to have a class 1 building, so we're done.

But now with respect to answer choice (E), note that either S or T could end up with the class 1 building F. Remember, we're given an unspecified number of trades, so T and S could swap F and G to their hearts' content.

The bigger point here for games is to start by considering the defining qualities of items in multidimensional games. Then work inward towards specifics.

[Adam Tyson]

Sure, but looked at with a longer lens, we know that R must have traded away their Class 1 building, and at some point they acquired two Class 2 buildings. Whether it happened in a single trade, or it happened after dozens or hundreds or thousands of trades, ultimately that is the effect - two Class 2s rather than the Class 1 with which they began. The outcome is what matters, not the exact path by which we got there.