How Logic Games Work

Back to: LSAT Logic Games

In the beginner’s mind there are many possibilities, in the expert’s mind there are few.

-Shunryu Suzuki

In LSAT logic games, the fundamental task is that of putting game pieces into spots on a game board, and that is what we want to get excellent at doing quickly and efficiently.

When you first encounter a game, and you are staring at a long list of rules, it’s easy to get intimidated at first.

Here’s a very typical basic ordering setup: During a period of exactly six consecutive days—day 1 through day 6—a handyman service will send one of its six contractors, L, M, N, O, P, and T to come work on a job site.

Even in this relatively simple example, there are over 46,000 possible arrangements. Overwhelming, right? During a period of exactly six consecutive days—day 1 through day 6—a handyman service will send exactly one of its six contractors, L, M, N, O, P, and T to come work on a job site. Each contractor will work on the project for exactly one day.

Did you notice the difference? It’s a subtle change, but the impact is enormous. Since each contractor will work on the project for exactly one day, we now know that each letter is used exactly once. This small addition to the scenario has narrowed our game down to 720 possible ways to arrange these six letters into these six spots.

And we haven’t even gotten to the rules yet.

Now imagine we are also given the following rule: N must work on the project on day 3.

With the addition of this rule, there are now only 120 possible arrangements.

Now, what if we stack on another rule? Let’s say that there is the following additional rule: There must be exactly one contractor between P and T, and P comes first.

There are now only 12 possible arrangements.

Now we’ll consider one final rule, for a total of three: M must come before O.

Given just three rules, the number of possibilities for this game is becoming very limited. In fact, there are only six possible outcomes.

We went from tens of thousands of possible combinations, down to just a handful. If you want, pause right here to map them all out. Here they are:

Just four scenarios cover all six the possibilities in the game. Note the O/L means that “O” and “L” can flip around in those scenarios. In total, there are just six orders that don’t violate any rules. From 720, three rules got us down to just six possible orders.

This is the essential, fundamental truth of how logic games work. We start with a ton of possibilities, then adding the rules narrows those possibilities way down until the game is much more manageable. Everything you do to solve a logic game involves this process of understanding how adding information about the order limits the possibilities. Everything.

There are a couple of reasons that understanding this is so critical:

First, it should keep you on task. When you’ve mastered logic games, all the thinking you are doing as you solve them is focused on this one narrow goal: understanding how rules and other information limits the order.

Second, it will help you stop being afraid of working with a lot of rules. When I started out on games, I was unnecessarily intimidated by games with a lot of rules. But after I realized what was going on, my perspective changed completely. Now I know that each additional rule narrows down the possibilities for the game a lot.

In general, the more rules in a given game, the simpler things become. I wouldn’t go so far as to say the rules are your friends, but really, they are there to help you out. That should be your mantra: THE RULES HELP ME OUT. How? By limiting possibilities.

Beyond that, the most common type of LG question will provide additional information about the order, then ask you to figure out how that affects the game. Hint: it’s always going to limit the possibilities even further. Returning to the setup above, here’s a typical question that might follow from that:

1. If L is last in the order, then which one of the following must be true?

When you get that new piece of info, plug it in, then see how the existing rules shape the game around the new information.

Where can our P_T block go? You typically want to look at any block rules you have first, as they very often can only fit in a couple of spots. Here, there is only one place for the P_T block: sandwiching the N:

Now, what about M and O? They, have to go in order, with M first. That means there is only one way to fit them in:

With four pieces of information—three rules, then the new information provided by the question about L’s location—we were able to determine the complete order for the game.

When answering LG questions, you’ll frequently see situations where the order is completely determined. If it isn’t completely determined, generally there will be just a few possibilities.

To reinforce the concepts here, make sure you watch the video below where we play through this narrowing of possibilities via the rules. The title, which is admittedly cheesy, is called “The Rules Are Your Friends.”

Hopefully, this should help you remember not to think of rules as some scary entity that is out to trip you up and ruin your LSAT score. They are ultimately manageable to work with, and each rule gives you information that further restricts the possibilities in the game, making life easier.

Always keep your attention focused on how the game is becoming more narrow, with fewer and fewer possibilities, and you’ll never get lost. Every phase of your attack is about working out how the game is becoming more restricted.

Within that context, let’s talk about the phases of attack. Here are the steps you follow to break down any game.

Again, for the sake of example, we use a lot of diagramming techniques in this next section, but you don’t have to make a conscious effort to remember them yet!