Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Defined—Moving, Balanced, Numerical Distribution, Identify the Possibilities game.

This game features seven flavorings included in two dishes (7 2). The first rule establishes a limitation on the number of flavorings in the appetizer (a maximum of 3), and thus the stage is set for a Numerical Distribution. Initially, the following distributions appear possible:

PT24-Dec 1997 LGE-G1-srd1.png

However, the second and third rules create two not-blocks (more on these in a moment), and because every flavoring must be used, these two rules mean that the appetizer cannot have 0 or 1 flavorings. Thus, there are only two possible fixed distributions in the game:

PT24-Dec 1997 LGE-G1-srd2.png

To recount, the 0-7 and 1-6 distributions are impossible because they would force either F and N, or S and T, or both together.

The second and third rules establish two not-blocks:

PT24-Dec 1997 LGE-G1-srd3.png

Essentially, each block results in a space in each dish being “reserved” for the members of each pair:

PT24-Dec 1997 LGE-G1-srd4.png

The fourth rule creates a block:

PT24-Dec 1997 LGE-G1-srd5.png

By combining the second and fourth rules, the additional inference that F and G cannot be included in the same recipe together can be drawn:

PT24-Dec 1997 LGE-G1-srd6.png

L and P do not appear in any of the rules, meaning they are randoms. That will be shown on the next diagram with asterisks. At this point, the diagram would appear as follows:

PT24-Dec 1997 LGE-G1-srd7.png

Because of the numerical distribution and the restrictive nature of the rules, this game can be attacked by Identifying the Possibilities:

PT24-Dec 1997 LGE-G1-srd8.png

There are only eight solutions to this game:

PT24-Dec 1997 LGE-G1-srd9.png

[hope]

I don't understand this setup at all. I would have only diagrammed A and M with the 3 - 4 diagram because the rule says that A got 3 at most. Where did the second diagram come from -- the A and M with 2 - 5? HELP!

[hope]

Hi It's Hope again. I guess I'm not understanding a basic concept about grouping games. When first approaching this game, I thought the rules would assign flavorings specifically to either A or M. So, are you saying that we can arbitrarily assign those flavorings ourselves? How do we know for sure that A gets certain flavorings and M gets certain flavorings? Am I getting Grouping construction mixed up with Linear construction?

[Tajadas]

Hi It's Hope again. I guess I'm not understanding a basic concept about grouping games. When first approaching this game, I thought the rules would assign flavorings specifically to either A or M. So, are you saying that we can arbitrarily assign those flavorings ourselves? How do we know for sure that A gets certain flavorings and M gets certain flavorings? Am I getting Grouping construction mixed up with Linear construction?

Hey Hope, I'm not with Powerscore but I think I can help. Some grouping games assign variables to specific slots, but this is not one of them, so yes, you can assign the flavorings however you want, so long as doing so doesn't violate any rules.

While Identifying the Possibilities is probably the fastest way to solve problems like these, I'm not very good at it. Instead, I made a crude 'basis' diagram. You may want to start there and then work you way up to the possibilities the administrator described.

Rule 2 tells us F and N cannot go to together. So I put (F/N) in the A column, and (N/F) in the M column, to indicate that if F goes in one column, N must go in the other, and vice versa. Because of Rule 3, do the exact same for S and T. At this point A has 2 slots (F/N and S/T) and M also had 2 slots (N/F and T/S). This is the basis for every possible answer.

Rule 1 says that A can have at most 3 slots. This means:
- Some answers will have 2 slots in A and 5 slots in M. Show this by adding 3 more slots to the M column. Fill in the remaining 3 variables G, L, and P. Because you just put G in the M column, N must also go in the M column (Rule 4), so remove the F/N and N/F symbols replace them with F in the A column and N in the M column. This solution becomes the first diagram the administrator showed.

- Some hypothetical solutions with a 3-4 distribution. I went back to the 'basic' diagram I created, which had 2 slots in the A column and 2 slots in the M column. I added 1 slot to the A column and 2 slots to the M column to create the 3-4 distribution. At this point, I stopped and answered the questions. However, you can make these 3-4 diagrams more detailed if you want. Consider the F/N and N/F symbols that are each in the A and M columns. If you select the N for the M column, Rule 4 says G must go along with it (see the administrator's second diagram). If you select N for the A column, G must also go in the A column (see administrator's third diagram). Draw one version with N and G in the M column, and another version with N and G in the A column. At this point, your diagrams should have 3 diagrams that all look exactly like the administrator's and you should be able to answer all the questions.

[Adam Tyson]

Thanks for the assist, Tajadas! You're exactly right about how to handle this game, although we would call it Identify the Templates, because in our jargon Identify the Possibilities would mean drawing out every possible solution, including variations with T in A and S in M and vice versa. As you saw, that's not needed here.

Hope, I don't have much to add to this excellent explanation, other than to say the assignment of variables isn't exactly arbitrary. There are many possible assignments, but they each come with their own set of rules and inferences, so making one choice generally has a domino effect on one or more of the other variables. Many games, including linear games, work just like that, so be prepared for a lot of open diagrams with a lot of flexibility in what goes where!