Setup and Rule Diagrams

[Jon Denning]

The second game on the June 2017 LSAT is a Basic Linear game, continuing the theme of Linearity from the first game. So for fans of order over groups things are off to a great start!

Specifically here we have seven musicians (L, M, N, O, P, S, T) being placed into seven performance spots, 1-7, with each person performing once and each spot filled. This is a nicely balanced 1:1 distribution, another reward for those hoping for a friendly first half.

The first four (of five total) rules exhibit some repetition, both in variables and construction:

Rule 1 has L ahead of N, while rule 3 also uses L and tells us there is exactly one space between L and O (we don't know their order). So that's:

L N
L/O __ O/L

Rule 2 has M ahead of T, and rule 4 repeats M with M and P separated by exactly one space (we don't know their order either). Together:

M T
M/P __ P/M

From these four rules very little is possible. Not Laws for N and T can be shown under space 1, and for L and M under 7...but that's really about it so far.

The we get rule 5, where P is either first or seventh.

On its own this is just a split option, but P has been used before: P is two spots away from M. So the fifth rule also affects M, and places either a P __ M block over spots 1-3, or an MTP block over 5-7 (remember that T is after M, so if M __ P is at the very end T must go in the middle).

This feels familiar to anyone recalling game 1, as we now have two options to potentially show Templates. Like game 1 we may not NEED to do Templates—we could simply note the M split and the general Not Laws, and think about the two paths and what happens to T in each and all the rest, moving quickly to the questions—but given the temptation, if not the outright wisdom, in Templates I'll lay them both out below.

Template 1: P in 1, M in 3

There's nothing we can place here definitively aside from P 1 and M 3, but some Not Laws do exist and they're worth noting:

T and N cannot be in 2. Both arise from the simple sequences, where T must be after M (M is in 3 here), and N must
be after L (N in 2 would force L into 1, but P is already there).

N cannot be in 4. With N in 4 L goes ahead of it in 2...but then L cannot be two spots away from O and thus we
have a problem.

O cannot be in 5. O and L are two apart, so O in 5 puts L in either 3 (M is there) or 7 (no room for N after it).

L cannot be in 7. This is always true; L is ahead of N, so L cannot be last.

S cannot be in 4. Toughest of the bunch, and easy to miss. S in 4 forces our L/O __ O/L block down into 5-7,
where L must be in 5 and O in 7 (L can't be last ever, don't forget). Why? Because neither L nor O can be in 2 if
S takes 4. Keep going: with L in 5 and O 7, N must be in 6 to comes after L...leaving only T available to fill 2. But
that's ahead of M in 3, breaking a rule. So no S in 4. (If you didn't catch this up front fear not, you either won't
need it or you can learn it later in the questions; I'm sharing for the sake of completeness)

Not what I'd call incredibly useful, but if you're quick to start on Templates and see at least the majority of those Not Laws without much hesitation it could be worth it.

It also would quickly fill in were you to be told certain things, say from a Local question. For instance, if L is 5th what happens? Well, that puts O in 7 and N in 6, meaning T must be in 4 (after M), and S is left with 2. The whole of this setup would fill in with that one small trigger. So sometimes Templates that look empty are a lot closer to complete than you might suspect

Template 2: M in 5, T in 6, P in 7

This possibility is a bit more powerful: we know where T must be, so we've filled in three of our seven spaces. We then get additional Not Laws as well:

N cannot be in 1. Another universal truth. L is ahead of N, so N isn't first.

L cannot be in 4. If L is in 4 then there's no room after L for N (MTP are in 5, 6, 7).

O cannot be in 2. Trickier, but this would place L in 4, and that's a problem as described in the line above.

S cannot be in 3. Again, definitely the hardest Not Law to see, and a forgivable one to overlook at the beginning
(if you missed it). What's wrong with S, our lone floater variable in this game, going in 3 here? Well, as above, S
restricts the L/O block: if S is in 3 that means the L/O __ O/L split block must be in 2 and 4, and no matter
what that forces N into 1 (it's the only variable left). N in 1 is always a problem, since it must be after L.

Another Template that feels a bit skeletal, but like the one above it won't take much to fill itself in. Imagine, for example, if S is fist: S 1 means we're in Template 2, first of all, so 5-7 are locked. It then puts the L/O block into 2 and 4, but to keep N after L we have to put L in 2, N in 3, and O in 4. Whoa. One variable gets placed and the rest fall in line. Powerful stuff (and useful; hint hint see question 11).