Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is an Advanced Linear Game: Balanced, Identify the Templates.

From the game scenario, we know that there are three variable sets: the five towns, the precipitation, and the order that the storm passes over the towns. Since the storm has a linear order, choosing that as the base is the most logical choice. This decision creates a linear setup with two stacks, one for the towns and one for the precipitation (remember to leave ample vertical space between the two stacks since each row will likely have its own Not Laws):

J05_Game_#3_setup_diagram 1.png

Because the rules have so many consequences, let’s examine each rule individually.

Rule #1. This rule is very straightforward and it can be represented by placing a “P” in the third space of the Town row:

J05_Game_#3_setup_diagram 2.png

Rule #2. This is another easy rule to diagram:

J05_Game_#3_setup_diagram 3.png

Rule #3. While the first two rules can be represented directly on the diagram, this rule must be diagrammed separately as two blocks. Of course, because L and O must have rain only, neither can be second:

J05_Game_#3_setup_diagram 4.png

The most obvious deduction that you should draw from this rule is that the two blocks can only be placed in the first, fourth, or fifth positions (the second and third positions already have conflicting information).

Rule #4. The final rule is sequential, and can be diagrammed as follows:

J05_Game_#3_setup_diagram 5.png

This rule is critical because it limits the placement of the towns, and ultimately leads to two templates. Let’s examine the implications of the rule more closely.

Because L and N must both be ahead of J, J can never be first or second. And, since P is already third, N must be the second town that the storm passes over, and either L or O must be the first town that the storm passes over; J must be fourth or fifth:

J05_Game_#3_setup_diagram 6.png

Reviewing the setup we have at this point, there are a number of limitations present. As in any game with restrictions, you should carefully consider if the restrictions are powerful enough so that taking a template approach would be optimal. In this case, we can create two templates based on the placement of J (J is chosen since it pushes L and N forward):

Template #1: J in the fourth position.

When J is fourth, L must be first, and O must be fifth. The only uncertainty in this template is the precipitation status for P and J.

J05_Game_#3_setup_diagram 7.png

Template #2: J in the fifth position.

This template has more possibilities than Template #1 because the exact placement of L and O cannot be determined.

J05_Game_#3_setup_diagram 8.png

With these two templates, answering the questions is easy.

[g_lawyered]

Hi P.S.,
I have a question regarding the opening paragraph of the game. The paragraph states

It passes over each town exactly once and does not pass over any two towns at the same time.

I originally thought that this could be interpreted as (and I wrote it down on the side) as:
r.... r or hr....,hr
Meaning that the precipitation of r.r being consecutive nor hr,hr being consecutive was possible. However when I solved the acceptability question and beyond I saw that the precipitations COULD BE consecutive. Meaning that hr,hr consecutively could be possible.
I'm sure I misunderstood this part of the game which is why the questions took me longer time to solve.
Can someone please interpret what that part of the game paragraph really means?

Thanks in advance!

[g_lawyered]

TYPO ERROR IN MY PREVIOUS POST:
What I meant was: Meaning that the precipitation of r.r being consecutive nor hr,hr being consecutive was NOT possible.

Thanks again!

[g_lawyered]

Also, Rule 3 assigning rain to L and O DOESN'T mean that ONLY L and O must have rain, correct? Rain could be occur in L, P, or J (but not in N). Am I understanding this correctly?

[Adam Tyson]

There's nothing in the rules or scenario for this game that prevents two consecutive towns from getting hail and rain or two consecutive towns getting only rain, GGIBA003@FIU.EDU . I'm not seeing where you got that inference. The portion of the scenario that you quoted only means that the towns are lined up in order and do not overlap or repeat, and it has nothing to do with what type of precipitation each town gets.

The rule about L and O does not mean that other towns cannot also get only rain. It would be fine if every town except the second one got only rain.

[g_lawyered]

Adam,
From your explanation, I see that the opening part I quoted refers to the towns variable (not the assignment of the precipitation variable). If I understood correctly, as you stated

that the towns are lined up in order and do not overlap or repeat,

. This part refers to the sequencing of the towns, part of the game, correct?

Thanks again for your help!

[Adam Tyson]

Correct! This game is an Advanced Linear game, meaning you are placing the variables in order and need at least two rows over that linear base. In this case, one row will represent the towns and the other will represent the type of precipitation that falls on that town, either hail and rain or else just rain. For example, the last town might be J and get just rain, or it could be J and get rain and hail, or maybe it's O and gets only rain.

[g_lawyered]

Got it. Thanks for clarifying that!