Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Basic Linear: Balanced game.

This is a fairly standard linear game, although the first two rules are unusual in that they jointly address all six variables. The first two rules create two not-blocks, and in each rule any two of the members can be consecutive, but all three members cannot be consecutive, regardless of their order. No Not Laws can be drawn directly from the two rules, but they clearly will play a significant role in the game.

The third rule can be diagrammed as H S, and two Not Laws are created, one for S under the first speech, and one for H under the sixth speech.

The fourth and fifth rules both include J. The fourth rule creates J Not Laws under the first and sixth speeches, and the fifth rule creates TJ and JT not-blocks. Because J’s speech must be second, third, fourth, or fifth from the fourth rule, when the fifth rule is considered, J’s options are limited by where T speaks, leading to two inferences:

• T3 J5
  and
  T4 J2

The information above combines to form the final diagram:

J95_Game_#1_setup_diagram 1.png

[DesignLaw806]

Wouldn't a third inference be possible for the fifth rule?

T2 --> J4

Therefore making another possible solution to the game?

H T S J K R

[Adam Tyson]

While that is a viable solution to the game, DesignLaw806, it is not based on a valid inference, because when T is 2nd, J doesn't HAVE to be 4th. J could, instead, be 5th in that case. Consider, for example:

HTSKJR

An inference is something that must be true, not merely something that can be true. Since T2 does not require J4, that inference is not valid. It's possible, but not necessary.

[DesignLaw806]

Thanks Adam!

After really looking at the not-block rules, it makes sense where the inferences come from based on where J cannot be placed.

[abutz]

Hi there! For some reason I am having trouble understanding one aspect of this game's set up and inferences with T and J. I made the right Not Laws, and then got to the T and J part and got totally confused on the homework explanation. TJ and JT cannot be consecutive / next to each other. J cannot be 1 and J cannot be 6. It says that J's speech must be second, third, fourth, or fifth from the fourth rule, and then it says when the fifth rule is considered, J's options are limited by where T speaks, leading to two inferences. Then it goes on to say T3 ---> J5 and T4 ----> J2
This is where I get confused. If the only rule is that TJ and JT cannot be right next to each other, couldn't J be in 3 and T be in 5, and J be in 4 and T be in 2? I just don't see where they got that T can only be 3 or 4 and J can only be 2 or 5, couldn't J also be 3 or 4 and T be 2 or 5? Please let me know what I am doing wrong! Thank you in advance.

[Stephanie Oswalt]

Hi abutz,

Thanks for your post! I have moved your post to the thread discussing this setup. Please review the official explanation and discussion above, and let us know if that helps, or if you have any additional questions! Thanks!

[abutz]

Hi abutz,

Thanks for your post! I have moved your post to the thread discussing this setup. Please review the official explanation and discussion above, and let us know if that helps, or if you have any additional questions! Thanks!

Thank you for getting that to the right place! I read the discussion above and I just don't get how J is limited because of where T speaks. If the rule is ~TJ and ~JT how do we infer that T would be T3 and J would be 5, and T4 and J2? I am so confused, I keep staring at the question and the rules and don't understand how that works.


I understand why T2 does not require J4, because the rule is just that T cannot be immediately before or immediately after J. So if T was 2 and J was 5, that would still be okay. But why aren't T’s options limited by where J speaks? Like since the rule is ~TJ and ~JT, I am not able to see why J is limited by T. I am so sorry, I don’t know why this is so hard for me to visualize and see.

So if T1, J just could not be 2, but it could be anywhere else, and if T2, J just couldn't be 3, but when T3, J HAS to be 5 since it cannot be 4 and cannot be 5. Is my thinking on the right track?

[Frank Peter]

Thank you for getting that to the right place! I read the discussion above and I just don't get how J is limited because of where T speaks. If the rule is ~TJ and ~JT how do we infer that T would be T3 and J would be 5, and T4 and J2? I am so confused, I keep staring at the question and the rules and don't understand how that works.

Since J can't be in the first or sixth slots, this is an inference that we can make based upon the limited spots still available for J. To be fair, this is an inference that not all students may pick up on when initially diagramming this game, but you may notice once you start testing out a few scenarios. The T3 --> J5 and T4 --> J2 inference would be especially powerful if you were doing a local question where the setup included T being place in 3 or 4.

But why aren't T’s options limited by where J speaks?

Because T has more spots that it can go than J does. For example, we couldn't say that J3 --> T5 because T could also go in 1 or 6.

[KG!]

Setup and Rule Diagram Explanation

This is a Basic Linear: Balanced game.

This is a fairly standard linear game, although the first two rules are unusual in that they jointly address all six variables. The first two rules create two not-blocks, and in each rule any two of the members can be consecutive, but all three members cannot be consecutive, regardless of their order. No Not Laws can be drawn directly from the two rules, but they clearly will play a significant role in the game.

The third rule can be diagrammed as H S, and two Not Laws are created, one for S under the first speech, and one for H under the sixth speech.

The fourth and fifth rules both include J. The fourth rule creates J Not Laws under the first and sixth speeches, and the fifth rule creates TJ and JT not-blocks. Because J’s speech must be second, third, fourth, or fifth from the fourth rule, when the fifth rule is considered, J’s options are limited by where T speaks, leading to two inferences:

• T3 J5
  and
  T4 J2

The information above combines to form the final diagram:

J95_Game_#1_setup_diagram 1.png

Again, like everyone else in the thread I'm still a little confused. I got pretty far in the game without that inference, so would you consider It necessary? Also, I understood that T3--->J5 for question #2. However, this was not an immediate inference I saw from the initial set up. How often should I be on the look out for this. I just didnt see it until the question played on our knowledge of that and even afterwards I didn't see how T4--->J2

[Jeremy Press]

Hi KG!

Certain inferences, like the inferences you mention about the positioning of T and J, are helpful when it comes to answering questions, but perhaps not necessary to see right off the bat when you're diagramming a scenario. I'd put these T/J inferences in that category for sure. As long as you saw them once you started diagramming in response to a local question, you're still in position to complete the game efficiently and accurately.

But if you spend a little time after the fact thinking about the inferences, you'll see they weren't overly difficult to arrive at even during the setup. First, J's being mentioned in two different rules leads me to think about J being a fairly limited variable. It only has 4 spaces it can occupy anyway because of the "not 1 or 6" rule. And J is further controlled by T. So think for a moment about where J will have to go if T is placed in certain positions:

With T in 2, J cannot be in 3 (next to it), so J would have to be 4 or 5.

With T in 3, J cannot be in 2 or 4 (next to it), so J would have to be 5 (there's your T3 J5 inference!).

With T in 4, J cannot be in 3 or 5 (next to it), so J would have to be 2 (there's your T4 J2 inference!).

With T in 5, J cannot be in 4 (next to it), so J would have to be 2 or 3.

Worth it to cycle through all those options before looking at questions? Maybe, if you can cycle through them very quickly. Otherwise, let the inference arise organically as you approach the local questions (and you'll likely not find yourself in any major difficulty from a timing or accuracy perspective).

I hope this helps!

Jeremy