# The Deal With That Trading Buildings Game

It’s rare in this world to find something that everyone can agree upon. In the hours after the December 2016 LSAT, however, we found something that fits the bill: the Logic Game about companies trading buildings was all kinds of f***ed up. Well, last week, as happens every year this time, the exam was released. And, of course, we got our grubby little hands on it immediately to take a gander at this oddity. To be sure, this game was weird.

It was an Operation Game, where you’re given an initial arrangement of variables and then asked to perform certain operations on them that will change that arrangement. Well, the particulars here were that each of three companies owned a few buildings. Each of the buildings was either Class 1, Class 2, or Class 3. To make this explanation easier, however, I’d like to tweak it a little and call them Class A, Class B, and Class C. (You’ll see why in a moment.) The rules were few and simple. You could trade any building for a building of the same class. You could trade one Class A building for two Class B buildings. Finally, you could trade one Class B buildings for two Class C buildings. That’s it.

Then they came out and started asking things like, after “some” number of trades, which of the following cannot be true. What the heck is that? Some? Like three? Five? Seven gajillion? Turns out there’s actually just one deduction that makes this about the easiest game of all time. Are you ready?

If a Class A building is worth two Class B’s, and two Class B’s are worth two Class C’s, then, by the transitive property, a Class A building is worth four Class C buildings. Look at it like this

A = B+B = C+C+C+C

If you look at Class C’s as the lowest common denominator, you can genericize the worth of each building. Now, here’s why I wanted to get the numbers out of the equation. Looking at it this way, a Class C building is worth 1 unit of value (whatever that value is), a Class B is worth 2 units, and a Class A is worth 4 units. In other words, the equation above looks like this.

4 = 2+2 = 1+1+1+1

Once you’ve done this, you’ll find that each company starts out with buildings that add up to 6 units. There’s no way that a trade can be done that will augment or diminish that total value. So, for example, the elimination question was monstrous if you try to slog through it the usual way, eliminating answer choices that violate a rule. But, once you’ve made this deduction, you just find and eliminate the answer choices that have one or more companies with buildings whose values don’t add up to six. This also straight up got you the answers to all the other questions.

As usual, they left this beast for the end, and having this flash of insight — or even just categorizing the game type — would take longer for most people than they had. The downside is that, if you’re studying for February or beyond, you may have this game type again. The upside is that you’ve seen it before.

Take note: the makers of the LSAT are going back to the Neither Games well a lot these days. Study games like this, and you’ll be ready for whatever they throw at you on test day.