Setup and Rule Diagrams

[Lina]

Hello, I am reviewing game #11 in February 1996, from LSAC's Superprep book. What kind of set up is required and what question type is this?

(This time around, I had a hard time getting through the LG's section, and identifying the best route to set up and while LSAC has explanations, I want to compare to powerscores since I prefer your method).

The seven members of an academic department are each to be assigned a different room as an office. The department members are professors F and G, lecturers Q, R, S and instructors V and W. The available rooms are seven consecutive rooms along one side of a straight hallway numbered sequentially 101 through 107. The assignment must conform to the following conditions:

Neither instructor is assigned to a room next to a professors room.
Neithe professor is assigned room 101 and neither professor is assigned room 107
G is not assigned a room next to R's room.
W is not assigned to a room next to V's room unless R is also assigned a room next to V's room

I diagrammed the base 1-7 to signify the rooms. Is the best way to keep the information organized, using subscripts for Professors, instructors and lecturers on the diagram? I noted the rules using subscripts.

[David Boyle]

Hello, I am reviewing game #11 in February 1996, from LSAC's Superprep book. What kind of set up is required and what question type is this?

(This time around, I had a hard time getting through the LG's section, and identifying the best route to set up and while LSAC has explanations, I want to compare to powerscores since I prefer your method).

The seven members of an academic department are each to be assigned a different room as an office. The department members are professors F and G, lecturers Q, R, S and instructors V and W. The available rooms are seven consecutive rooms along one side of a straight hallway numbered sequentially 101 through 107. The assignment must conform to the following conditions:

Neither instructor is assigned to a room next to a professors room.
Neithe professor is assigned room 101 and neither professor is assigned room 107
G is not assigned a room next to R's room.
W is not assigned to a room next to V's room unless R is also assigned a room next to V's room

I diagrammed the base 1-7 to signify the rooms. Is the best way to keep the information organized, using subscripts for Professors, instructors and lecturers on the diagram? I noted the rules using subscripts.

Hello Lina,

It's an advanced linear game. Without doing the whole set-up (which might prevent you from doing the set-up yourself and getting the practice), some ideas:

1) The good old Separation Principle could be of use here re instructors and professors;
2) Instead of subscripts, you could try making multiple stacks, say, for professors, instructors, and lecturers, above the base. See how that works. (In advanced linear games, multiple stacks are often the way to go, rather than subscripts; e.g., subscripts may be difficult to see, and putting things in stacks may be a more usable visual representation.)

Hope that helps,
David

[LSAT2018]

I know the separation principle in concept, but have difficulty applying it. In the context of this game, would the separation principle apply to the rule neither instructor is assigned to a room next to a professors room?

And what were the inferences for this game? I only found that the professors (F and G) were very restricted, but that was all.

[Adam Tyson]

That's exactly the rule that the separation principle might apply to, LSAT_2018, although it does so somewhat imperfectly, because while the Professors cannot sit next to the Instructors, it may be that the Professors could sit next to each other and the Instructors could also sit next to each other (as would happen in the last rule).

There aren't any major inferences that come directly and obviously out of the rules here. With no sequencing rules we don't get any obvious not-laws, and there are no rules that tell us who can or must be in any particular space. In a situation like this, you have two choices: 1) try one or two hypotheticals to see what happens, perhaps gaining a deeper understanding of the game along the way, maybe making a key inference or two; or 2) dive into the questions, noticing that a lot of them are Local questions for which you will likely be drawing out scenarios anyway.

Either approach is valid here. While I think most people would head into the questions quickly, and would do just fine doing so, I happen to be obsessed with trying "what-if" scenarios. If you are able to do them quickly, they can be a great benefit. While I am not saying you must do this, here's one that I would try: what if V is at space #4? I chose this because it will have an impact on several other variables, pushing the two Professors away from the middle but also raising questions about the last rule about WVR (which may in turn impact the GR rule). So, here I go:

With V, an Instructor, in space 4, the two Professors are forced into positions 2 and 6, in either order. Wait a minute...where can I put W? W, another Instructor, cannot go next to Professors F or G, but every available seat right now is next to one of them. Holy cow, V cannot go 4th! And for the same reason, neither can W! Now we're cooking! There's the separation principle at work in a big way! (This also directly answers one of the global questions, so bonus).

In fact, looking at this hypothetical, I can see that there is no way that the two Professors could ever be in spots 2 and 6. They will have to be closer to each other than that. If I try them in spots 2 and 5, or else in 3 and 6, I'll run into the same problem - at least one Professor will have to sit next to at least one Instructor. They have to get closer still, such as in spots 2 and 4. That will work if the two Instructors are next to each other in spots 6 and 7, or the mirror image of that could happen with the Professors in 4 and 6 with the Instructors in 1 and 2. Both of these will trigger the last rule about WVR. This exercise will also directly answer another global question and give you plenty of ammo to attack at least one of the local questions.

So, while this "what-if" approach wasn't required, speaking for myself I found it to be entirely worth the time an effort. I came away from it with a better understanding of how all the rules interact with each other, as well as a few scenarios that I can use to answer a good chunk of the questions without having to do much, if any, additional diagramming. Consider adding a little "what-if" process to your diagramming routine and see how it might benefit you in the long run. It's not always going to pay off in as big a way as this one did for me, but with practice you'll get a feel for when you should try it and which "what-if" questions you should ask yourself.

Give that a try, and good luck!

[Shonan]

I think there might be a quick way to find that F and G either block together or separated by only one lecturer.

We are told that Professors cannot be 1 and 7, which means wherever a Professor goes, there are two people next to him.
we also know only Lecturers(L) can be next to Professors(P), so whenever is a Professor, there is a LPL block.
However, there are only three L, we cannot have LPL(space)LPL, so the game board must either be LPLPL, or LPPL.

[Adam Tyson]

Nicely done, Shonan! Either the Professors are next to each other, bounded by Lecturers, or they are separated and part of an LPLPL block with the Instructors on the ends. Well done, and I have nothing to add but applause!