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 Dave Killoran
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#40800
Setup and Rule Diagram Explanation

This is a Basic Linear: Balanced, Identify the Templates game.

This game is remarkably similar to the second game on this test. In this game, six vehicles are serviced over the course of six days, one vehicle per day. Thus, this is a Balanced Basic Linear game with the following initial setup:

PT63_Game_#3_setup_diagram 1.png
Similar to the prior game, there are again four rules. Let us examine each in detail.

The first rule can cause some diagramming confusion. The rule suggests a sequence is in play, as at least one vehicle is always serviced later in the week than the hatchback. However, instead of diagramming the rule as H :longline: ___, the best representation is to show the functional effect of the rule, namely that H can never be serviced last:

PT63_Game_#3_setup_diagram 2.png
The second rule creates a standard chain sequence:

..... ..... ..... ..... ..... ..... ..... ..... V :longline: R :longline: H

As with all three-variable chain sequences, six Not Laws are created:

PT63_Game_#3_setup_diagram 3.png
However, because we know that H cannot be serviced last from the first rule, the latest that H can be serviced is Friday. Operationally, the effect of this rule combination is that the last three Not Laws from the second rule “slide” over one day, to Thursday and Friday:

PT63_Game_#3_setup_diagram 4.png
Saturday, which already cannot be a day when H is serviced, is also off-limits to V and R. Adding these three Not Laws back into the diagram creates the full Not Law set from the first two rules:

PT63_Game_#3_setup_diagram 5.png
Note that already the last position is becoming restricted, and is down to the triple-option of L/P/S.

The third rule creates an unusual block, one where P is always serviced consecutively with S or V, but not both. This creates four separate, exclusive block possibilities:

PT63_Game_#3_setup_diagram 6.png
Essentially, then, there is either a rotating PS block, or a rotating PV block, but SPV and VPS are precluded. This can be diagrammed in various ways, including:

PT63_Game_#3_setup_diagram 7.png
No Not Laws can be drawn from this rule.

The fourth rule creates two mutually exclusive possibilities:

PT63_Game_#3_setup_diagram 8.png
Two inferences can immediately be drawn from this rule, namely that S can never be serviced first (because S is always serviced later than P or later than L) and S can never be serviced last (because S is always serviced before L or before P):

PT63_Game_#3_setup_diagram 9.png
When added to the prior two rules, this results in the inference that only L or P can be serviced last:

PT63_Game_#3_setup_diagram 10.png
As in the last game, let’s examine the scenarios that result under each possibility.

Template #1: ..... P :longline: S :longline: L

Under this option, L must be serviced last because only L and P could be serviced last, and P must be serviced earlier than L in this scenario. With L being serviced last, the first five days must meet the following conditions:
  • 1. ..... V :longline: R :longline: H

    2. ..... P :longline: S

    3. ..... PV or VP or PS (SP is impossible since P :longline: S)
The two sequences will be shown on the diagram, meaning that only the PV/VP/PS block from the third rule must be tracked:

PT63_Game_#3_setup_diagram 11.png
Template #2: ..... L :longline: S :longline: P

Under this option, P must be serviced last because only L or P could be serviced last, and L must be serviced earlier than P in this scenario. When P is serviced last, then either V or S must be serviced on Friday, to satisfy the third rule. However, because V must be serviced earlier than R and H from the second rule, V cannot be serviced on Friday, and thus S must be serviced on Friday:

PT63_Game_#3_setup_diagram 12.png
The remaining four variables are H, L, R and V. From the second rule, H, R, and V are in this sequence: V :longline: R :longline: H. L acts as a random as it already satisfies the L :longline: S :longline: P sequence because S and P are serviced on Friday and Saturday, respectively. This results in the complete diagram for this template:

PT63_Game_#3_setup_diagram 13.png
Combining all of the prior information creates the final setup for this game:

PT63_Game_#3_setup_diagram 14.png
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 z0egreen
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#78462
Ah you lost me here: However, because we know that H cannot be serviced last from the first rule, the latest that H can be serviced is Friday. Operationally, the effect of this rule combination is that the last three Not Laws from the second rule “slide” over one day, to Thursday and Friday

Why are the restrictions sliding over by one day?

and here: When P is serviced last, then either R or S must be serviced on Friday, to satisfy the third rule. 

The third rule is the P, V, S consecutive rule so not understanding the connection there.
 Jon Denning
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#78522
Hi z0e — thanks for posting! Let me tackle those questions individually to hopefully clear things up!
Ah you lost me here: However, because we know that H cannot be serviced last from the first rule, the latest that H can be serviced is Friday. Operationally, the effect of this rule combination is that the last three Not Laws from the second rule “slide” over one day, to Thursday and Friday

Why are the restrictions sliding over by one day?
That V -- R -- H sequence "slides" to spots earlier in the week to avoid placing H, the final variable in the sequence, on Saturday, since the first rule tells us that H can't be last. That is, normally a sequence like that could fill the final three positions—Thursday to Saturday—but here if we tried to put the VRH sequence on Thursday/Friday/Saturday, then H would be the final vehicle and we'd break the first rule. So the latest we can have V would be Wednesday, the latest for R is Thursday, and the latest for H is Friday (to avoid it being on the final day). The Not Laws simply reflect the positions that those three variables cannot go: V after Wednesday, R after Thursday, and H after Friday.
and here: When P is serviced last, then either R or S must be serviced on Friday, to satisfy the third rule.

The third rule is the P, V, S consecutive rule so not understanding the connection there.
Apologies, as that's a typo in the original explanation (that I've fixed): the "R" references in that paragraph should instead be "V," as the third rule has P next to either V or S.

I suspect that likely resolves any (understandable) confusion about that portion of the setup, but if not please let me know!

I hope that helps!
 Queziam
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#81397
Thank you so much for this explanation!
 mostofthetime
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#83474
Hi there, thank you for your explanation!

I was wondering how you knew to put the V-R-H sequence before the P-S sequence in temp #1 ? AKA, why isn't
P-S-V-R-H-L allowed?

When I looked at this I could definitely see the use of two templates given P-S-L | L-S-P but my templates are not even close to filled out because I blanked on the next step. I thought basically anything was possible after those were placed.

And couldn't you split V-R-H up and keep the PS block together and do something like V-R-P-S-H-L? Since it's not a block, just a sequence?
 Adam Tyson
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#83536
I was wondering how you knew to put the V-R-H sequence before the P-S sequence in temp #1 ? AKA, why isn't
P-S-V-R-H-L allowed?
The template we provided actually DOES allow for that solution, mostofthetime! It can take a little getting used to, but the comma inside those parentheses should be read as the word "and". What that template is saying is "in these first five spaces you will have V before R before H AND you will also have P before S." It doesn't mean the VRH sequence has to precede the PS sequence, but just that both sequences will coexist in those five spaces somehow.

And couldn't you split V-R-H up and keep the PS block together and do something like V-R-P-S-H-L? Since it's not a block, just a sequence?
Absolutely you can do that! Just as long as you have that P next to either the V or else the S, but not both, and you comply with both of those sequences, you're good to go!

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