Setup and Rule Diagrams

[momgoingbacktoschool]

Sorry, when I tried to align that rule it didn't appear correctly. Is it H --> H/S (H/S = H and S in the same week) or S--> S/H?

S --> S/H

[momgoingbacktoschool]

Setup and Rule Diagram Explanation

This is an Advanced Linear, Underfunded, Unbalanced game.

Below is a basic diagram of the setup (scroll down within the picture to view the entire list of diagrammed rules). There are several points to note.

1. The linear component to the game is structured around the four consecutive weeks, which constitute the base.

2. In each week two paintings must be shown, one oil and one watercolor. Because the scenario and rules don't require a determination of which painting comes first in a given week, it is arbitrary which type of painting is placed on top and which on bottom in the diagram.

3. The game is underfunded. There are only 3 oil paintings, each of which must be shown at least once, meaning to fill the 4th week, one oil painting must be shown twice. The same is true of the watercolor paintings.

4. Since no painting can be shown in consecutive weeks, there are only a limited number of options for which weeks the paintings shown twice can be shown. They will be shown twice in weeks: 1 and 3, 2 and 4, or 1 and 4. While there isn't an efficient way to depict that in the setup (templates are not a productive option for this setup, because there are too many possible solutions), it is helpful to make the inference and keep an eye on it in any given solution.

5. Because Gold and Ping cannot be shown together, and because there must be at least one week in which H and S are shown, it cannot be the case that both Gold and Ping are shown twice (though one of them could be shown twice).

6. The final rule is a complicated "unless" form of conditional rule. Use the PowerScore "Unless Method" for diagramming unless statements. Step one is to make the "unless" clause the necessary condition. Here, "I is shown in week 1" is the necessary condition. Step two is to negate the remaining condition and then diagram it as the sufficient condition. The negation of "H cannot be shown earlier than the third week" is "H is shown earlier than the third week." In "if-then" terms the rule therefore means "If H is shown earlier than the third week (in week 1 or week 2), then I must be shown in the first week." Since I must be shown in the first week if this rule triggers, that means there is no possible scenario where H can be shown first (hence, the "Not Law" in the diagram). From the third rule, wherever H cannot be, S cannot be either, meaning we can also diagram a "Not Law" for S in week 1. Putting all the above information together, the basic takeaways from this rule are that H and S cannot be in week 1, and if H is shown in week 2, then I must be shown in week 1. The contrapositive is that if I is not shown in week 1, then H must be shown in week 3 or week 4.

Screen Shot 2020-04-20 at 10.20.49 AM.png

so, what you're saying is, we can't really come up with too many templates except that when H is in 2 then I is in 1. the way to do this game is to just attack each question by diagramming the info provided in the stem?

[KelseyWoods]

Hi all!

@ncolicci11 and @cmorris32:
Yes, you are correct that you can infer that G R, because G cannot be with P and S can only be with H. And yes, that inference only means that if you have G, then R must be with it, but you could still have R without G. R could be with either H or I as well as G.

@j199393:
The 3rd rule is that "Hanbok must be shown in any week in which Sails is shown." Remember that "must" is a necessary indicator. In this case, "must" is modifying H, so H is necessary for S. Thus, we would diagram the rule this way:

S H

(You can actually see that diagramming if you scroll down on the setup image above.)

@momgoingbacktoschool:
Yes, I wouldn't use the template strategy for this game because there are too many possibilities in terms of the pairings and the order. Templates are great, but they shouldn't really be your default strategy. Most games aren't very conducive to efficient templating. So as you're practicing, take care to always consider whether or not templates are actually useful for the various games you attempt.

Hope this helps!

Best,
Kelsey

[startedfromKZnowwehere]

Hi there,

Would someone mind explaining inference #5 in the "Administrator" post above?

Thanks!

[Dave Killoran]

Hi there,

Would someone mind explaining inference #5 in the "Administrator" post above?

Thanks!

Hi Started,

For the purposes of explaining this, the separate four weeks here can be seen as groups:

• ___      ___      ___      ___
  
  ___      ___      ___      ___

If G and P were both to be used twice, but they can't be in the same week, then from a grouping standpoint they would take up a space in each week (again, this isn't in order, just by how you could arrange variables in four separate groups):

• ___        ___         ___       ___
  
  _G_      _G_      _P_      _P_

Now, we know that when S is used, then H must be used. S will have to appear in one of the four groups above, and when it does, there won't be room for H. And that's why G and P both can't be doubled.

Thanks!

[startedfromKZnowwehere]

Thanks David! I appreciate it.

[santony27]

Please read the uploaded attachment and please help me figure out Q 13 - Q 16.

The uploaded attachment contains my understanding of the rules, my deductions, my scenarios in my deductions and why I do not answer the correct answer choices for Q 13 - Q16. - I am having issues uploading a word document so listed below is my explanation.


PT 87 Q 11-17 – Please read on – I have trouble with Questions 13 – 16 – Please read my deductions and then read the highlighted Questions that I am having trouble with

4 consecutive weeks
3 oil paintings  G,H,I
3 watercolor paintings  P,R.S

Each week – 1 oil painting & 1 water color painting
Every painting must be shown once
No Same painting in consecutive week

If G (oil) is shown then ~P (watercolor) - ~GP
If H(oil) is shown then S(watercolor) --HS
~H in week 2 unless I in week1 -- Clearly H in week 1 makes no sense when I is being shown in week 1

Oil ---- ---- ----- ------
Watercolor ---- ---- ----- ------

Deductions
1. 6 paintings Total in 4 weeks -- one set is repeated
2. One HS
3. No GP
4. As combinations it is valid for us to see

Crafting 2 Scenarios where I is in 1st week and the other where I is not
__¬I__ __H__ _G__ __H__
__P__ __S___ _R__ __S__

__¬I__ __G__ _H__ __G__
__P__ __R___ _S__ __R__


Now for Scenario where I is not in week 1
Clearly in this scenario H cannot be placed in week 1 nor can I which leaves only G in 1 and I in 2
H can be only in week 3 or week 4
We have a rule that H must be placed with S however there is no rule stating that S cannot be placed with any other letter
HS in week 3
_G__ __I__ _H__ _I/G__
_S__ __P/R_ _S__ __P/R__ clearly week 4 must be IP/GR

HS in week 4
The second sub scenario is
_G__ __I__ _G__ _H_
_R__ _P_ _R__ __S_

Answers to Questions

Based on my Scenarios
Q11 – clearly C is the answer

Q 12 if S is in week 2 – I can see the listed below 3 scenarios
Pretty obvious too – Clearly Handbook cannot be shown in week 3
_G__ __H__ _I_ _ G__
_R__ __S_ _P__ _S__

_I__ __G__ _I_ _ H__
_R__ _S_ _ P__ _S__

_G__ __H__ _G_ _ I__
_R__ __S_ _R__ _P__

Q 13 I have trouble with the MUST BE FALSE
Option A - Sails is shown in first week – To me it is true see below
_G__ __I__ _H__ _I/G__
_S__ __P/R_ _S__ __P/R__ clearly week 4 must be IP/GR

However the answer is that Option A must be false – can u help me see why???


Q14 – If Gold is shown in first week

_G__ __H__ _I_ _ G__
_R__ __S_ _P__ _S__

As per the combination above Ibex is shown in 3rd week why is Option A not the right answer


Q 15 When is the complete order of elements determined

_G__ __H__ _I_ _ G__
_R__ __S_ _P__ _S__

In the above answer both Sails is shown twice and Gold is shown twice why is it one or the other. I can also have H shown twice as follows:
__¬I__ __H__ _G__ __H__
__P__ __S___ _R__ __S__


Q16 – If Rolls is shown in Week 2 and Week 4

_G__ __I__ _H__ _G_
_S__ _R_ _S__ __R_

In this scenario I is shown in week 2. Why is Option D not the right answer??

[Adam Tyson]

Hey santony27, this is a lot of work, and I hate to burst your bubble, but you started out with a misunderstanding of the rule about H and S. It's not that H requires S, but that S requires H. S cannot be with G or I, but H could possibly be with R or P if H goes twice. And since S can only be with H and G cannot be with P, G can only be with R.

To see our setup for this game and our analysis of all the questions, go to this thread:

viewforum.php?f=1307

But before you do, I suggest working through the game again after correcting that H/S rule. I have a feeling you'll do just fine with it! Good luck!

[SGD2021]

Hello,

I am getting a bit confused about the 4th rule (conditional involving H and I). In post 5 in this thread, Adam wrote: "Your idea of I showing in weeks 1 and 3 looks entirely possible! S would have to be shown in week 2 with H (because otherwise we could not have S in the game at all), R would have to be shown in week 4 with G (because G cannot be paired with either P or S), and P would have to be shown in week 3 with I (because S cannot be with I and we cannot have R twice in a row). The only thing left uncertain in that case would be the Watercolor in week 1 - it could be P or R."

However, I do not understand how it is possible to put I in week 3 when we have S and H in week 2, with I in week 1. If I goes in week 3, wouldnt that mean (according to the rule) that I is not in week 1, so H must be in 3 or 4, so H must go in 4 (since I is already in 3) but it can't be since then we wouldn't have anywhere to place G? Or is it that the sufficient condition of the conditional rule (I is not in 1) doesnt get triggered since we already have an I in 1?

[Adam Tyson]

An important consideration in this game is the numerical element, SGD2021. One watercolor will have to be shown twice, and one oil will have to be shown twice. If H is in week 2, I must be in week 1, but it could be the oil painting that goes twice, in which case it could be show in week 3 or week 4. Once we place an I in week 1, that necessary condition has been satisfied, and adding another I somewhere else doesn't violate that rule. So, here are some possible combinations with I going twice (and these are not the only ones):

IHIG
PSPR

IHGI
RSRP

IGIH
PRPS

IGHI
PRSR

And of course there are solutions with G going twice, and with H going twice, too.