Whenever I talk to people about the LSAT, I almost inevitably hear the same thing: “Logic games were my favorite section.” It baffles me. Not to put too fine a point on it, but I don’t love logic games. I dislike them them so much, in fact, that I often wished someone could save me from them. Enter LG superhero, Playing the Numbers.
Playing the Numbers is a powerful method for confronting certain classes of games. While the tactic isn’t applicable to all or even most games, it can crack open a game in no time, allowing you to pick up easy points and bank time for other games.
There are three steps involved in playing the numbers: recognizing the challenge, looking for principles of distribution, and doing the math (coincidentally, math might be the only thing I hate more than logic games—naturally, the two would intersect…).
The first step involves looking at the type of game that you’re tasked with solving—if it has an uncertain distribution, then this is a pretty good indicator that you might want to play the numbers. Generally speaking, there are three types of games that call for playing the numbers: underbooked (fewer players than slots) or overbooked (more players than slots) games, games with players from different categories (e.g. cats and dogs, girls and boys), and unstable grouping games (games where the size of the group is unknown). If you see one of these games, it is not a sure bet that you’ll wind up playing the numbers, but it is a pretty good indicator.
Next, if you determine that you might benefit from playing the numbers, you’ll want to look for principles of distribution. In order to do so, you should know how to differentiate principles of distribution from other rules. Most rules will simply give you some information about what player goes where; principles of distribution, however, will restrict the distribution of variables. In other words, they’ll tell you how many times a variable can appear, how many variables can be selected from a category, or how many players can be assigned to a group. They often contain words and phrases like “at most,” “at least,” “exactly,” and the like. If you see these types of rules in one of the games mentioned above, you should immediately be thinking about playing the numbers.
Finally, you’ll want to do the math. When you’re making your set-up, you always want to distribute the larger variable set into the smaller variable set. For example, a game might ask you to spread out five players among three groups. You always want to start with the most extreme distribution. Continuing with our example, and assuming there is no upper or lower limit on the number of variables that can appear in a given group, the most extreme distribution is 5-0-0. From there, you want to work toward the most equal distribution of variables: 4-1-0, 3-2-0, 3-1-1, 2-2-1. Here, any shift merely repeats one of the previous distributions, so you know you’re done.
Once you use the principles of distribution to do the math, you should have a much better handle on the different ways a game can play out. Furthermore, using this strategy can lead to important deductions along the way.
In a nutshell, the telltale signs for playing the numbers are (1) games with uncertain distributions and (2) principles of distribution. Despite my deep hatred for all-things logic games related, I have an even deeper appreciation for this strategy and for the clarity it can bring to the process. Take it from this apparently crotchety law student, you’ll want to master this strategy if you hope to succeed on the LSAT. Up, up and away!