Setup and Rule Diagrams

[Jon Denning]

Let me walk through this setup (rules and a few key inferences) in text form below in hopes that this helps any readers out!

First, this is a Basic Linear game, with 1-7 as the base and the variables R, S, T, U, W, X, and Z moving around it. Since it's balanced (7 into 7) we don't need to worry about distributions, duplicate usages, or empty spots.

The first rule simply produces a Not Law for T under spot 1.

It is connected to the second rule too, where we get a large T __ __ W block and several Not Laws: T cannot be in 5, 6, or 7, and W now cannot be in 1, 2, 3, or 4 (note W not in 4 because that would force T in to 1 and break the first rule).

This is also the moment in the game where the idea of creating templates becomes potentially appealing: the T __ __ W block only has three possible positions—in 2 and 5, 3 and 6, or 4 and 7. Each of those may be well worth exploring, provided that the remaining rules produce further results based on the TW block's placement. Let's see if they do.

Next, we get two rules that are duplicates of one another: S and Z must be kept apart, and W and X must be kept apart. These "not blocks" as we call them tend to be weak rules and typically have no immediate effect in games, and that's precisely what happens here. In neither case can we determine where any of those four (S, Z, W, X) variables go, nor can we make additional Not Laws about them. In short, these two rules don't give us much, and require that we know where an involved variable is placed before we rule out the positioning of others (that is, if we know S is in 2 we could know that Z can't be 1 or 3, but without that S trigger we've got nothing).

So we'll keep those rules in mind as they'll no doubt be tested, but there's nothing to show in the diagram and they give us little when it comes to filling in our templates further, if we choose to go that route (granted they would produce Not Laws for X next to the W in the TW block, but that's really it).

Finally, the last rule gives us a rotating UX/XU block. We don't know their order, of course, but we do know that they require two consecutive spaces, and that's useful, particularly if we try to place the block between T and W since W and X can't touch (it would have to be TXUW if U and X are inside that block).

So we've arrived at what I believe to be an interesting—and slightly subjective—crossroads. On the one hand you could choose to move into the questions with a fairly skeletal setup, just Not Laws for T and W and a working knowledge of the remaining rules. This is certainly the faster option at this point, as no further diagramming is required. However it's likely going to make the questions more challenging since we have so little definitively shown at the outset.

The alternative option is to commit to the templates I noted above, focusing on the placement of the UX block in/around the larger T __ __ W block. These will absolutely take some time to create, and it's certainly possible to succeed in this game without them. However, since I know some people will choose to do templates here (or at the very least will be curious about them as they read this), I'm going to lay out the various scenarios below.

Again, the large T __ __ W block is the template trigger here, as it only has three possible positions. Let's look at those three, and then see what we can fill in for each (possibly branching into additional templates if more either/or splits arise):

1. T __ __ W in 2 and 5:

With T in 2 and W in 5, there are two places for our UX block to go: between T and W in 3 and 4, or after W in 6 and 7. Let's show each, remembering that W and X cannot be adjacent, and also accounting for the S Z separation that we need:

S/Z T X U W (Z/S, R) [note that either S or Z must be in 1, as putting R in 1 would force S and Z next to
one another in 6 and 7, leaving R and either S or Y to fill the last two spots]

S/Z T (Z/S, R) W U X [again, we have S or Z in 1 and the other, with R, between T and W to keep them apart]

2. T __ __ W in 3 and 6:

Now we have a similar situation the one just seen, where UX can go either between T and W (4 and 5), or in front of them (in 1 and 2, in either order U/X).

U/X X/U T (R, S/Z) W Z/S [the UX block in 1 and 2, in some order, and S/Z in 7 so they're kept apart]

(R, S/Z) T X U W Z/S [the UX block is in 4 and 5 between T and W, with S/Z in 7]

3. T __ __ W in 4 and 7:

This is the most uncertain option with regards to the UX block. It has three possible positions: 1 and 2, 2 and 3, or 5 and 6.

U/X X/U S/Z T (R, Z/S) W [here we have the UX block in 1 and 2, in some order, and S/Z in 3 so they're kept apart]

S/Z U/X X/U T (R, Z/S) W [UX in 2 and 3, with S/Z in 1]

S/Z R Z/S T X U W [with the UX block in 5 and 6, R, S, and Z take the first three spots, with S and Z separated by R]


So that's 7 different templates we've drawn, which are no doubt a huge help, but also a tremendous investment time-wise. Whether they're worth it is up to you (personally I don't think I'd write them out, but for some people it'd be the right call).

I hope that helps!

[wrjackson1]

From this setup, could you draw the inference that R must always be next to S/Z, and if so, is it worth it to make this time investment? I find that I'm either A)running out of time or B) jumping into the questions unprepared and making stupid mistakes. Thoughts?

[Jamena Pirone]

Hi wrjackson,

While you are right that R must always be next to an S or a Z, I suspect that one would only realize this after having constructed the seven templates that Jon outlined above. If you choose to go the route of drawing templates, and you have filled in every slot with its respective possibilities, then you should not spend time looking for further inferences therein.

The goal of looking for inferences is to allow you to go a few steps further in your understanding of how the game could play out. However, by constructing templates, you have effectively written down every possible way the game could play out. There is nothing left to infer! Once templates are done, you should move directly into the questions with the knowledge and confidence that you have already written the answer-- all you need to do for each question is find where you wrote it.

This should help shave a few seconds off the time it takes to complete this type of game.

Happy studies!

[kyunglt]

Hi. Can someone please post the setup, answers and explanations to this game? It really helps.

Thanks.

[ncolicci11]

What language would be needed for it to be T_W? T is two chapters ahead of W?

[Jeremy Press]

Hi ncolicci,

Yes, although they'd probably phrase it something like: "T is mentioned exactly 2 chapters before W is mentioned." Of course, they were careful with the wording here, probably to avoid the possibility of ambiguity. So they might just have stuck with the language they chose, and instead said: "T must be mentioned before W, and there must be exactly one chapter separating the mention of T from the mention of W."

Happy studying!

Jeremy