Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Basic Linear Game: Balanced.

October 97_M12_L3_explanations_game#1_setup_diagram_1.png

[tthauvette]

Hello,

In having taken a full length test over the weekend, one of my weak areas has come up as local logical game questions. I have gone back to some of the lessons to strengthen that area. Having said that, I am here again picking the same wrong answer I picked the first time. I think I am over analyzing or oversolving these. Can you help?

Question is: If M fills some track before that of J and also before that of K on the recording, which one of the following must be true?

I pick B each time. The correct answer is (D). I know that is correct but I thought we were solving for

M<<<<J
K

this is what I had diagrammed:

/k/h/g F /k/j/g/h/l /l/m /m/k
1 2 3 4 5 6 7

M would have to go in 5 and because J can't go in 7 it would go in 6 therefore, leaving k in 7 and answer choice b?


Any help would be appreciated.

thanks,

Tania

[Adam Tyson]

Hey there Tania, I think I see what you are doing wrong there, although a portion of your question is hard to read as a diagram (one of the shortcomings of using this text-based forum for questions about diagrams, I know).

In this local question, M must be SOMEWHERE before both J and K. That does not mean that M must be IMMEDIATELY before J or K, nor does it force J and K into being in that exact order, nor does it mean that M is not before anything other than those two things.

From the original diagram, we learn that M could be as early as 4th position. This question requires that M now go no later than 5th, but it could still go 4th, as long as it is before both J and K. Imagine an order like this one:

HFLMKJG

J cannot go 7th, but G still may, so answer B is not supported here in this Must Be True question. Notice that K and J would be interchangeable in this diagram - there is no implied order between those two variables in the question, just that they must both be after M. Sure, K COULD go 7th, but it doesn't have to, because G is also able to go there.

Does that clear things up? Be sure not to assume anything that is not supported by the rules. Just because something is before something else does not mean that it must be immediately before those things, or that it is before only those things.

Keep at it, you'll get there!

[tthauvette]

Yes the light bulb went off when I was studying last night. I would call this a breakthrough for me because I think I have been doing this more than once and leaving points on the table because of it. Your response total clears it up.
I am sure this won't be the last post I have as I dig deeper into the games.

thanks,

Tania

[Marce]

HI,
RE: GAME 1 SET UP
Where did the G SUBSCRIPT 4 -----------> H SUBSCRIPT 1 DERIVE FROM?
THIS RULE WAS NOT EVEN COVERED IN LESSON 3 FOR THE CURRENT ONLINE COURSE, BUT IS DIAGRAMMED IN THIS SET UP.
PLEASE RESPOND ASAP, AS THERE WAS A DELAY GETTING ME SET UP FOR THE FORUM ALL MORNING.

[Dave Killoran]

Hi Marce,

Thanks for the question! First, the G4 H1 representation is conditional, and conditional reasoning was covered in Lesson 2 (and will be seen many more times!). Perhaps it's the subscript that threw you off, but that is a reference to the seven numbered spaces for the music pieces. In a game like this, when you see numbers, look to connect them to any other numbered set. In this game there is only one, which is the seven numbered spaces.

So, the next question is where did this inference come from? As you noted, it's not stated directly in the rules. Thus, it is something that can be drawn from a combination of the other rules and restrictions. In class, sometimes this inference gets covered, but sometimes not depending on time. But we always include every inference—even the small ones—simply so you can look at it afterwards and think about it In this case, this is a very tough inference to make, and it is not one that most people make during the setup, nor one that they are required to make (hence why it is sometimes not covered during class). Let's take a look at how we draw it:

• When G is placed 4th, from the third rule we know that H is affected. Now H is a very powerful variable, because L and M must follow behind it in a sequence: H L M. So, we want to take a close look at where H could be, especially any time G is placed since G pushes H around via the third rule. So if G is 4th, then H is automatically knocked out of 3rd and 5th.
  
  6th and 7th are also out of the picture, simply because the H L M sequence leaves no room (and these Not Laws are always covered during class).
  
  So, that leaves just 1st and 2nd, but 2nd is taken up by F (from the first rule). Thus, almost surprisingly, when G is 4th, the only remaining position for H is 1st. To best capture that relationship, we write it out in conditional form: G4 H1.

Please let me know if that helps. Thanks!

[Marce]

Hi Dave,

Im still confused about the choice of G4--------->H1 being made as an inference from this game; essentially G can be 1st and H can be 3rd and then L, M can follow, NEXT J and K. So I don't agree with this inference made on this game, it just threw me off.

[Adam Tyson]

I think you might be misinterpreting that inference, Marce. It doesn't mean that G is always 4th and H is always 1st. It means that IF G is 4th, then H is 1st. That is, if you should ever place G at 4, H would have to go to 1. This is because they cannot be next to each other, so H cannot be at 3 or 5 in that instance, and H can never be later than 5th because it still has to be before both L and M. With F taking up the 2nd slot, H has nowhere left to go but 1st when G is 4th.

That's conditional reasoning, by the way. The use of the arrow signifies that the element to the left of the arrow is an "if" statement, which is called a Sufficient Condition. The element to the right of the arrow is the "then" part of the relationship, called the Necessary Condition. The diagram indicates that G in the 4th position is sufficient to prove that H must be in the 1st position.

You are correct that G can be 1st. G can actually be in any position except 2nd! H can be 1st, but can also be 3rd, 4th or 5th. It's just that when we put G 4th, H then must be 1st. Inferences like that can be very useful and powerful when you get to the questions, and that's why we encourage you to look for them in the diagramming process.

I hope that clears up the confusion!

[Tajadas]

Is there a way to make this game into templates? I tried but didn't get very far, though at least it helped me see that G4 H1

[Adam Tyson]

It is possible, but there would be too many to make it worthwhile. Imagine, for example, building templates around where we place H, since H is somewhat restricted by the H-L-M sequence. If H is first, what does that tell us? What about if it is 3rd? It's really only when it is 5th that some pieces fall perfectly into place, and even then either J or K could be 4th.

Reserve the template approach for games that are clearly divisible into two or three (and once in a great while, four) "starting positions," with each of those starting positions having some defined impact on other variables.