This blog post covers one common, yet simple, technique for listing all the options/templates/possibilities in Basic Linear and Advanced Linear games.
Let's say we're doing an 7-slot / variable Linear game in which only one variable can go in each slot. This means we're placing the game's 7 variables (ABCDEFG) in some kind of order.
Just to keep this short and sweet, let's pretend all the other rules, inferences, and limitations have filled up (determined the placement of variables into) slots (spaces) 1, 2, 6, and 7, giving us:
We have 3 empty slots, and we have three variables (A, B, C) we haven't placed yet.
Let's also pretend we have a rule telling us A is before B. We can diagram this as:
Because we have 3 variables remaining, 3 slots remaining, and we know 1 of these 3 (A) is before another of these 3 (B), we know there are only 3 main possibilities for the game.
How do we find these? Limited Options.
We place A and B first because we know the most about them. We don't know anything about C. C is a wild card variable.
We can place A and B into the diagram in the following 3 ways:
D E A B _ F G
D E _ A B F G
D E A _ B F G
These are the only 3 possibilities for the placement of A and B.
We can now place C into the empty slots, giving us:
D E A B C F G
D E C A B F G
D E A C B F G
I would just stack those three bolded possibilities into the diagram like this:
(I wouldn't actually number them, of course.)
LSAT Logic Games give you scenarios where this technique applies more often than you'd think. There have even been cases where it applies to the main diagram for Advanced Linear Logic Games (example: PrepTest 37, Game 2 - page 305 in Next 10). However, it more frequently comes up as something you can do for specific scenarios / hypotheticals in both Basic Linear and Advanced Linear games.
So, just keep this in mind: when there are 3 slots remaining, 3 variables remaining, and 1 of those variables most go before another, there are only 3 possibilities, and they're worth drawing out, whether it's for a main diagram or a specific scenario.
Photo by 10458725@N02 / CC BY-NC 2.0