Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping Game: Defined-Fixed, Balanced, Identify the Templates.

June 02_M12_game#3_L5_explanations_game#5_setup_diagram_1.png

The key to this game is the interaction of the last two rules. Because no two books from the group of V, P, and S can be on the same shelf, each book must occupy a different shelf. And, since there are only three shelves, we can infer that one book from the group of V, P, and S must be on each shelf:

June 02_M12_game#3_L5_explanations_game#5_setup_diagram_2.png

Thus, the first shelf is occupied by either V, P, or S; the second shelf is occupied by either V, P, or S and one other book; the third shelf is occupied by either V, P, or S and two other books.

The interaction of V, P, and S also affects the other three variables, F, H, and W. Using Hurdle the Uncertainty, because the first shelf is occupied, F, H, and W must be on the second and third shelf:

June 02_M12_game#3_L5_explanations_game#5_setup_diagram_3.png

The only remaining “active” rule is the first rule. Thus, the placement of F must be carefully tracked, and in fact, depending on the placement of W, there are only a few possible templates:


Template #1: F on the second shelf

June 02_M12_game#3_L5_explanations_game#5_setup_diagram_4.png

Because F must be on the same shelf as V or W, V must be on the second shelf. P and S form dual-options on the first and third shelves.

Template #2: F on the third shelf, W on the second shelf

June 02_M12_game#3_L5_explanations_game#5_setup_diagram_5.png

Because F must be on the same shelf as V or W, V must be on the third shelf. P and S form dual-options on the first and second shelves.

Template #3: F on the third shelf, W on the third shelf

June 02_M12_game#3_L5_explanations_game#5_setup_diagram_6.png

Because F and W are on the same shelf, the first rule is satisfied, and thus V can be assigned to any one of the three shelves.

In total, these three templates contain ten total solutions, and using these templates makes the game considerably easier. However, the game is still time-consuming because there are seven questions.

[eveitch]

I'm do not understand how you determined to use three templates. Can someone explain in more detail how he knew to use three templates?

[Francis O'Rourke]

Hi Eveitch,

Forming templates can be very helpful on games, but they are not always necessary. For example on this game, as long as you came close to seeing the inferences that the administrator posted at the following level, you should make it through this game with ease:


In general, we can make templates when one rule leads to a small number of possible outcomes, and when these possible outcomes lead to helpful inferences. In this game, because F must always be accompanied by either V or W, we can a lot of what also occurs when F is placed on the middle shelf, and we can learn a few more things when we place F on the bottom shelf. The only way to see this is through looking over the rules and recognizing limited possibilities and, of course, practice. Although setting out these three templates can be very helpful to complete the questions, it is not necessary to draw them out before we go on to the questions.

[jmramon]

Hi,

How do you guys know that V, P, or S should go into the sections you boxed and F, H, or W must go into the other boxed section? I also fear that if I used this template, I would get confused as to whether it means V, P, "and" S must go into those sections or whether its an "or" situation. Could you please clarify what your template means and how you reached such inferences without trying hypothetical solutions? My template also looks a lot different than yours, and via hypotheticals I figured out that W, F, and H cannot be placed into shelf #1. Your template also seems to indicate that only V, P, or S can be placed onto shelf #1, but how did you magically figure this out without hypotheticals? I'm having a lot of difficulty with figuring out these inferences without hypotheticals and the games therefore take me way too long. Thanks for the help, as always, Powerscore!

-Jenny

[Alexandra Ruby]

Hi Jenny,

Since there are only 6 variables going in to 3 shelves and since there are restictions on 3 of them, S, V and P, providing that they cannot be in the same group together, you can immediately make the first inference that one of S, V and P needs to go on each shelf. More specifically, S cannot be with P, S cannot be with V and V cannot be with P. Thus, you need to split these 3 amongst the 3 shelves. If you put either S, V or P on shelf 2 or 3, the rules push the other 2 variables into the 2 other shelves. Thus, you have to reserve 1 spot for S, V and P on each shelf.

Once you have "reserved" these 3 spots for S, V and P, you know that one of them takes up the 1 spot on shelf 1. Shelf 1 is now "filled" with one of S, V or P.

Moving to shelves 2 and 3, we now know we have to reserve one spot on each shelf for one of S, V or P and, thus, only have 3 spots remaining for F, H and W. Because of the F V/W rule, you know that there are only a few variations of how F, H and W can be arranged.

But to answer your other question about running hypotheticals first, no, you should not be doing that as your first line of attack. In grouping games, typically when there are rules restircting two or more variables from being in the same group, you will have to spllit them and reserve a spot for them in each group (similar to the S, V, and P rules in this game). Then, you determine how many variables you have left and see where they can or cannot go depending on the rules that apply to them (similar to the F, H, W situation in this game). This is how you "Hurdle the Uncertainty" and make quick inferences.

Hope this helps!

[Vexans]

Are there any clues we can look for when diagramming a game that might indicate that using a template will be useful? I see how much it helps to solve this game but I know that this is certainly not true for all games. I am worried that on test day I may waste a lot of time drawing templates that end up not being useful.

[AthenaDalton]

Hi Vexans,

The decision of whether or not to draw a template will vary based on the game.

In general, I take the time to draw out templates when there is a rule that creates two (or at most three) clear branches in the game. For example, a linear game with a lot of variables linked together like this (AB_ _ C _ D) might give you a rule that says "B must be in either space 3 or space 5." With that clear-cut rule, it makes sense to draw one template with B in space 3 and another template with B in space 5, just to see how the rest of the variables fall into place.

This game also lends itself to drawing templates since there are so many limitations on which books can share shelf space. Once we know that one book is on the middle shelf, a lot of the other variables fall into place.

If you're in doubt about whether you're in a template game or not, feel free to start things off with the rules question and see how that goes. If you're really struggling to answer the first question, it can be a sign that your setup needs more work. In either case, don't get stuck! If you're not finding many inferences in the setup phase, it's a clear sign that it's time to move on and start answering questions.

I hope this helps clarify things. Good luck studying!

Athena Dalton

[davidp95]

How can I get better at coming to these inferences? I feel like if my life depended on, I could have not arrived at this of VPS go? tbh I am so frustrated that I cannot make these inferences.

I am thinking backwards now that it is being explained: Would I say okay well since P and S cannot go together, they must go into separate shelves so it could be 1-2; 2-3: 1-3.

and then when V comes along because those two variables also do not go with each other, I can say well V would go into the one that PS did not go to?

[Luke Haqq]

Hi davidp95!

Your reasoning seems to make sense to me. In addition, if you have PowerScore's lesson books, I can suggest a couple of lessons that might be useful.

The first is lesson 5. Among other valuable tips that this lesson gives for grouping games, it addresses the Hurdle the Uncertainty concept. This concept is in play with respect to the inference about V, P, and S in this game, so familiarizing yourself with it could be useful to do. The lesson also has several grouping games that you might consider doing as drills.

The second is lesson 9. This lesson addresses games with limited possible options, where it might make sense to diagram the templates or all possibilities. Diagramming the templates/possibilities can be time consuming, thus it comes with a risk. But you might find in starting to diagram out some possible scenarios will bring to light inferences that you might not have noticed at first. The lesson also contains several games to drill yourself on, which can help in improving your ability to draw inferences, as well as your ability to spot game types where it might make sense to diagram the templates/possibilities. Here, there's a comparatively small number of variables, they're all used, and there are rules significantly constraining where they can be placed.