Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Basic Linear: Balanced game.

Initially, this game looks promising, as exactly seven investors view a building site on seven consecutive days, creating a Basic Linear scenario:

PT27-Dec 1998 LGE-G1srd1.png

The first rule creates an F split-option on days 3 and 5:

PT27-Dec 1998 LGE-G1srd2.png

Although F cannot then view the site on any other day, we will not show those Not Laws as that information is redundant.

The second rule creates L Not Laws on days 4 and 6:

PT27-Dec 1998 LGE-G1srd3.png

The third and fourth rules are conditional:

PT27-Dec 1998 LGE-G1srd4.png

More on these rules later in the discussion.

The final rule creates an HG block:

PT27-Dec 1998 LGE-G1srd5.png

From this rule we can infer that G never views the site on day 1, and H never views the site on day 7:

PT27-Dec 1998 LGE-G1srd6.png

At this point, the rules have been represented, so the next step is to check for any linkage between rules.

One link occurs between the third and the fifth rules, which are connected by H. When J views the site on day 1, then from the third rule H must view the site on day 2, and from the fifth rule G must view the site on day 3:

PT27-Dec 1998 LGE-G1srd7.png

However, when G views the site on day 3, this affects the first rule, forcing F to view the site on day 5:

PT27-Dec 1998 LGE-G1srd8.png

At this point, four variables have been placed, and only three days remain available for viewing the site—day 4, day 6, and day 7. Because L cannot view the site on day 4 or day 6 from the second rule, L must then view the site on day 7. At this point, only two variables remain unplaced—K and M—and only two days are open—day 4 and day 6. The placement of L in turn affects K. Via the contrapositive of the fourth rule, when L does not view the site on day 5, K cannot view the site on day 4. Thus, K cannot view the site on day 4, and must view the site on day 6. M, the random, is the last remaining unplaced investor, and M must view the site on day 4. Therefore, when J views the site on day 1, only one solution to the game exists:

PT27-Dec 1998 LGE-G1srd9.png

Another link occurs between the second and fourth rules, which are connected by L. However, as the fourth rule places L, no further inference can be drawn from that relationship. The fourth rule also links to the first rule through day 5. When K views the site on day 4, then L must view the site on day 5. Via the first rule, this affects F, who must then view the site on day 3:

PT27-Dec 1998 LGE-G1srd10.png

The placement of F on day 3 further affects the third rule. If F views the site on day 3, then J cannot view the site on day 1 because there would not be sufficient room to allow H to view the site on day 2 and then G to view the site on day 3. Hence, when F views the site on day 3, J cannot view the site on day 1:

PT27-Dec 1998 LGE-G1srd11.png

When all of the information is combined, including the fact that M is a random, the following diagram results:

PT27-Dec 1998 LGE-G1srd12.png

[srcline@noctrl.edu]

Hello

So I initially thought this game was pretty straight forward basic linear game, but I started running into some problems.

So here is my setup.

1 2 3 4 5 6 7

F is either 3 OR 5
lOPEZ cant be in 4 or 6

Jday 1 Hall visits site 2
(+) if Hall does not visit site 2 Jones does not view the site on day 1

Kday4 Lday 5
(+) If L does not view the site on day 5 K does not view the site on day 4

Block: HG

Is this correct so far. I know I have to be missing some inferences.

Thankyou
Sarah

[Dave Killoran]

Hi Sarah,

That is correct so far—well done! The next step here is to consider how some of the common elements link together. for example, look at the first and fourth rules: they both contain a reference to "day 5." Is there a way that they could be connected? Yes, there is: If K is on day 4, then we know that L is on day 5. What would that then to do F? From that first rule, it would force F to be on day 3, leading to the following inference:


K4 L5 + F3


Are there any other connections like that that you can see? There are

The first step in making inferences is to connect together common variables and elements from two or more rules. Almost every game allows you to do that, and it's a fast and relatively way to start seeing how things fit together. Think of it like dominoes: you are trying to see how things fall into place one after the other; you just need to find a starting rule and then see what connects to that rule.

I hope that helps. Thanks!

[David Boyle]

Hello

So I initially thought this game was pretty straight forward basic linear game, but I started running into some problems.

So here is my setup.

1 2 3 4 5 6 7

F is either 3 OR 5
lOPEZ cant be in 4 or 6

Jday 1 Hall visits site 2
(+) if Hall does not visit site 2 Jones does not view the site on day 1

Kday4 Lday 5
(+) If L does not view the site on day 5 K does not view the site on day 4

Block: HG

Is this correct so far. I know I have to be missing some inferences.

Thankyou
Sarah

Hello,

Pretty much, though some other inferences can come from placing the HG block at various places. For example, if you place it at 2 and 3, and put J in 1, then F must be in 5. So L can't be in 4 or 6, and neither can K be in 4, because that would put L in 5, where F is. So M must be in 4, K in 6, and L in 7. That solves a lot, obviously. (Including question 2, maybe)
Also, if you put K in 4, and L in 5, then F must be in 3. Then the HG block could go in 1-2 or 6-7.
So try putting various combinations together, and see what happens.


David

[srcline@noctrl.edu]

Hello,

Thankyou both for explanations.

So far I got

K4 L5 + F3

J1 Block HG

IS this correct?

Thankyou
Sarah

[Nikki Siclunov]

Sarah,

This is correct, but terribly incomplete. There is a great deal of additional inferences you can make if you play a bit with the conditional rules.

For instance, what if J is 1? Clearly, we know that H will be 2, and - given the block - G will be 3. Recall, however that F must be either 3 or 5. So, in that case F must be 5. What about L? L cannot be 4 or 6 (second rule); consequently, it must be 7. Furthermore, from the contrapositive of the fourth rule, we know that if L is not 5, K cannot be 4. Clearly, then, K cannot be 4, and must therefore be 6. M is left to be 4:

J1 J H G M F K L

I wouldn't want to solve the entire game for you, but hope this gives you an idea of what we're looking for when we talk about inference-making.

Thanks!

[studyhelp20]

Hello Power Score Support Staff,
Can you please provide me with a more straightforward picture diagram of the correct setup, rules, and inference for this game? It is hard for me to visualize the complete diagram setup, rules, and inferences from the previous questions that were asked. Thanks for the help.

Sincerely,
Brennan

[KelseyWoods]

Hi Brennan!

I'll give you the basic diagram for the rules, but this game has many possible inferences that I'm going to challenge you to explore for yourself first! Once you have some inferences, you can ask us to confirm that your inferences are correct. But the only way to get better at inference making is to work on making them yourself

Screen Shot 2020-12-15 at 12.10.43 PM.png

A couple of hints/tips to get you started:
Start with your conditional rules.: If J is first, you know H is second. What does that mean for your other rules? If J is first, you can actually figure out where every other variable goes. See if you can do it! Then find out what happens if K is 4th--this scenario should end up with 3 possible orders.

Hope this helps! Good luck inference-making!

Best,
Kelsey

[VamosRafa19]

Hi,

I understand if you guys don't want to go through all the inferences and what not. My question is if it advisable to start plugging in a bunch of scenarios during a time crunch? I understand plugging in J in 1 is easy enough and is a good place to start. Then K in 4 is also a good place to start. But after that how much do we want to keep going? Even after plugging those in there's still a lot of scenarios left. How far down the rabbit hole do we want to go in terms of making possibilities and inferences in a conditional game like this? Obviously the questions address a lot of these scenarios but not all? So is it worth trying to identify all of them?

[Robert Carroll]

Vamos,

Unless I were trying to do templates, I would probably only do the hypotheticals you talked about. You're also right that the questions are all (excepting the first) local, so they're inducing minidiagrams anyway.

As for why I wouldn't do templates, I don't see any great reasons to do them. I have two choices for F, but neither one seems to lead easily to any other inference. The conditionals are going to be tough to make templates from - we'd need three templates for each (reflecting the three possibilities allowed by a conditional - that its conditions are both true, that they are both false, and that the sufficient is false while the necessary is true).

Robert Carroll