Stabilizing Unstable Grouping Games

Recent administrations of the LSAT have seen an uptick in a certain type of Logic Game that we at Blueprint like to call unstable grouping games. If that phrase seems like a string of gibberish to you, here’s an example of the type of game we’re referring to:

Jack, Susie, and Dexter are splitting up their Halloween candy. Their neighbors are cheap jerks, so they only got one of each type of candy. The types of candy are: Hershey’s, Junior Mints, Kit Kats, M&Ms, Reese’s, Skittles, and Tootsie Rolls. Each kid gets at least one type of candy, but they’re kids and, you know, Dexter is a bit of a bully, so the candies won’t necessarily be split up equally.

Games with this type of set-up seem formidable because, at first blush, it doesn’t seem like you have much information — it’s easy to find yourself staring at a mostly-blank set-up and wondering how in the world you’ll ever be able to answer such detailed questions.

As is so often the case, the answer is: deductions! And the secondary answer is: Playing the numbers! Basically, since we know so little about the size of each group, you’re looking for any crumb of information that the LSAT deigns to give you, so if you see what we call a “principle of distribution” about the size each group can be, you’re gonna scoop that right up.

In the above example, let’s say you have a rule that states that Dexter gets four types of candy (hey, I said he was kind of a bully). Great! Now we know the size of one group. But wait, there’s more — you want to think about the implications on the other group sizes as well. If Dexter gets four candies, then that leaves three to be split between Jack and Susie. Each kid gets at least one candy, so either Jack gets two and Susie gets one, or vice versa.

Now we know that there are two potential ways the game can work (the one where Jack gets two and Susie gets one, or the one where Jack gets one and Susie gets two). And it sure seems like there is something we usually try to do when there is a limited number of ways a game can work… if only I could think of what it was called…….

I kid, of course. This is a prime instance for scenarios! So you’d jot down two separate diagrams, one for each possibility, and fill in as much of each diagram as you can – and voila! You’re ready for the questions.

The principle of distribution varies by game, but the key thing to remember is that in an unstable grouping game, you should always be thinking about whether there is anything that limits the size of any group. The more you can figure out about how many players are in a group, the more you’ll be able to find deductions. In some cases you’ll be able to use that information to create scenarios, but sometimes it’ll just be helpful in the questions (for instance, because you’ll know that a certain group is full, or close to being full). Either way, you’ll no longer be staring at a mostly-blank piece of paper, and that makes all the difference.

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