Setup and Rule Diagrams

[Jeremy Press]

Setup and Rule Diagram Explanation

This is a Defined (Moving) Grouping game, with a significant distributional component. It's also a game in which there is some real value to using the Identify the Templates technique.

A few notes on the setup and templates:

1. The rule involving P and S functions to create a block in this game. This is because each variable must be used exactly once. Thus, in the one group where P is assigned, S must also be present. And there is nowhere else S can be assigned (since it can only be used once).

2. Since all 6 textbooks are edited exactly once, but we only know that each editor edits "at least one" of the textbooks, we have uncertainty about the distribution of the 3 remaining textbooks. The setup further fixes the distribution by assigning H exactly two textbooks to edit. Since F and G each must edit at least one textbook, there are only two possible general distributions of the remaining 4 textbooks to those two, a 3-1, or a 2-2.

3. It's worth sketching out each general distributional option at the start. In the F=3, G=1, H=2 distribution, we don't get a lot of additional information about where the variables go, but we do know that the PS block cannot be assigned to G, who only edits one textbook in this template. Further subdividing this template into 2 options is possible, if not completely necessary: one where the PS block and L/Z are assigned to F (in which case, M will be assigned to G, and R and one of L/Z will be assigned to H); another where the PS block is assigned to H (in which case the other variables are more flexible in placement).

4. The F=1, G=3, H=2 distribution is impossible, because there is nowhere M can be assigned. It can never be assigned to H. It can only be assigned to G if it is the only textbook assigned to G. And it cannot be assigned to F, because F must edit at least L or Z. Templating is thus very valuable because it exposes the impossibility of this distribution.

5. The F=2, G=2, H=2 distribution is relatively detailed. M must be assigned to F (along with L/Z), since it cannot be assigned to G where G edits more than one textbook. There must be a group of P and S (since wherever P is assigned, S will go). And there will be another group of R with L/Z. We don't know where the PS and R-L/Z groups will be assigned but knowing they are present confers significant advantage when it comes to this distribution.

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[180bound]

HI!

Can someone help me with the set up of this game?
I have a feeling that numerical distributions are going to be important here but I can't deduce anything from the set up (or any of the questions) that would restrict the game to a single distribution like I thought would....My guess is I missed something important in the set up.

Thanks!

[Jeremy Press]

Hi 180bound,

This is a Defined (Moving) Grouping game, with (as you correctly anticipated!) a significant distributional component. It's also a game in which there is some real value to using the Identify the Templates technique.

Diagrams of both the initial setup and the possible templates are now posted above.
Please let us know if you have additional questions, based on these notes and diagrams!

[1997law]

Why does rule #5 create a block? I thought the wording of this rule made it clear that "the editor of the psychology textbook must also edit the statistics textbook," rather than the other way around. In other words, I don't understand how one of the editors must also edit the psychology textbook if they edit the statistics book.

[Robert Carroll]

1997,

The scenario says that "each textbook must be edited by exactly one editor". Whoever's doing the psychology textbook must also do the statistics textbook, as per the rule. But whoever that is, it's the single person who's doing the statistics textbook. So it's also valid to say that whoever does S does P, which is why the block is an appropriate representation.

Robert Carroll

[npant120]

Hello,

I used the PS block to separate the game into 4 templates: 1 with PS in F, 1 with PS in G and 2 templates with PS in H: one where G was editing M and one where F was editing M. Is this a reasonable approach to take? I was able to answer all the questions in time, but I am just wondering if I happened to get lucky or if this was a fair approach. I do sometimes struggle with whether to use the distributions to template vs. using specific rules (ex. placement of blocks) to template when both are relevant to the game so I'm not sure if there happens to be a good rule of thumb here.

[Hanin Abu Amara]

Hi!

That is a great approach! Way to go figuring it out. As for using templates and distributions, keep practicing it. There is bit of a learning curve as to when you should or should not attempt templates but the more you try, the better sense you get for when it's the right thing to do.