Setup and Rule Diagrams

[Jon Denning]

Setup and Rule Diagram Explanation

The section begins with a whimper: a relatively easy Advanced Linear game, where five photographers (F, G, H, J, K) and their five photo essay themes (R, R, R, U, U) form two stacks above the base, 1-5.

There are two ways to attack this game.

First, you can take a more traditional approach, simply diagramming the rules, basic inferences, and Not Laws:

R in a space above 1, a KF block (so K not 5, F not 1), G in 3 (so K also not 2, and F not 4), a JU vertical block
(with U above J in the block if your upper level is R/U), a Not Law for J under space 1 (since 1 is an R)...

Note that I skipped the third rule about F and K being different types intentionally, to give it a little further discussion. Essentially since there are only two types, R or U, then we can turn this rule into two conditionals:

FR KU
FU KR

Showing it in terms of positive events, instead of as Not Blocks (like FUKU , for instance), makes it easier to see when it would come into play: as soon as we know either F or K's theme, we know the other. They're always opposites, where one gets an R and the other gets a U.

Also, and this is a nice inference, knowing the number of themes in play—3 R and 2 U—affects this rule, as well, since J always gets ones of the two Us, and either F or K must take the other one! Our two Us are taken then, one by J and the other by either K or F. That means that both G and H must be Rs! (Always pay close attention when you have a small-numbered variable set, like just two Us or three Rs, or even a base as limited as only five spaces!)

With those rules and inferences in place, you would likely be successful in moving immediately to the questions and beginning to collect your points!

However, there is a further step you could take at the outset if you choose to: Templates. And that's the second possible way to attack this game.

With G in the 3rd spot our KF block only has two possible placements: we could put it in 1 and 2 (before the G), or in 4 and 5 (after the G). In either case the remaining variables, H and J, would get pushed to the back or the front, and knowing that H is always an R (see above) and that J is always a U (the final rule) allows you to fill in even more!

Let's take a look at both templates.

Template 1: KF in 1 and 2

R U R R/U U/R
K F G H/J J/H

Here the first three spots are filled by K, F and G, and since we know that the first spot (with K) is always R (rule 1), and that K and F cannot have the same theme (rule 3), then F in 2 must be a U.

Further, G is always an R (discussed above), leaving only the uncertainty of where H and J will go, 4 or 5, with their respective themes, R (for H) and U (for J).

This template leads to just two possible solutions based on whether 4 and 5 are H and J, or J and H.

Template 2: KF in 4 and 5

R U R (R/U)
H J G K F

This second template option is also extremely well filled in, with the order of the photographers completely determined: with K and F taking 4 and 5, H and J have to go into the first two spots. And since J is always a U, then H must be in 1 since 1 is always an R. Put another way, we can never have J in 1, so if H and J are the only options for spot 1 it must be H.

That means H in 1 is an R, J in 2 is a U, G in 3 is an R (G is always R, remember), and the only uncertainty is what K and F in 4 and 5 will be: one will be the other U, and one will be the third R. We can't know which is which, so I showed it above as a split option in parentheses for spots 4 and 5 (we know R and U go to those spaces, but not their exact assignments).

Again we have a total of just two possible solutions, depending on whether 4 and 5 are R and U, or U and R.


The choice to pursue templates or not is entirely your own, and should be based on how comfortable you feel without them—if you can confidently tackle the questions without templates then don't bother showing them!—and the amount of time you anticipate them taking—time is precious, so if you're routinely running out of it, and again feel like you'd survive with a more modest upfront setup, templates become harder to justify.

Regardless, this was a very favorable start to the June 2017 LSAT, and the well-prepared earned 6 quick and easy points.