On a quiet evening, my wife and I were sitting with our kitties in front of the fire. Warm, happy, and loved, there was no more perfect time to reflect upon LSAT logic games...
There is a well-known logic problem. It has many forms, but I like it best adapted to my field. It goes like this:
A Philosophy department was seeking a new Chair. There were three candidates for the position (that's how you know it's fiction: there would never be THREE candidates for being Chair. Someone has to be dragged kicking and screaming into the position and kept there with cookies.). To decide the next Chair, the Chairperson declared there would be a logic contest.
"I have three white hats, and two black hats," she said. "In a moment, I shall take the three of you into the conference room. I will then place a hat on each person's head, either White or Black. Only, there's a catch. The room is pitch black. The windows are covered, and the light is off. In the darkness, you will not be able to see the hat on anyone else's head, and you will not know the color of the hat that is placed on your own head. The first candidate to correctly identify the color of the hat that MUST be on their own head shall be the new Chair."
The Chair and two of the candidates got up from their seats and began to walk into the pitch black conference room. The third candidate remained seated. "Aren't you coming?" asked the Chair. "No need," the candidate replied. "I already know what color my hat must be." Shocked, the Chair gestured for the candidate to proceed. "Do tell," she said. The candidate gave her answer, and was elected the new Chair on the spot.
What did the candidate say?
(To help, there are no "gimmick" answers or trick responses, e.g. "she said her hat was black because all of the hats are black in a dark room." No nonsense like that. Just standard logic.)
I've given this riddle to my classes for years. Not one has ever gotten it right (without Googling it...). What is remarkable is that it is not a difficult riddle at all. In fact, I would argue it's not even a riddle, but a testament to your state of mind. You have to see the world a certain way. And if you CAN see the world that way, you have the most important ingredient in solving logic games quickly and accurately on the LSAT.
For the record, Bumblebee growled, Kik threw up, and Echo rolled over. The wife, after two glasses of wine, threw a pillow. That is the sum total of their answers.
From the military to business, I often hear versions of the old acronym, KISS: Keep it simple, stupid!
Simplicity is always the problem. Logic games often appear simple upon reflection. Students read "unlocked" logic game solutions, or watch YouTube videos, or buy prep books, and it always seems so simple. Every inference is laid out. All of the connections you missed in the frenzy of the test are now apparent. "Oh, if only I had seen that inference!"
I'm reminded of chess. We amateurs marvel at the games of Grandmasters. Their solutions are so elegant, their combinations brilliant. It looks, in retrospect, so simple when the game is laid out before us, commentary in hand. "If only I could see what they see! If only I could calculate moves in advance like the Grandmasters!"
Both Alekhine and Reti, two very different Grandmasters, were asked the same question: "How many moves ahead do you calculate when you play?" Alekhine, who was famous for long, brilliant continuations, answered "Twenty." Reti, famous for his irritation, answered "one." Chess amateurs aspire to have the nearly godlike calculative powers of an Alekhine, calculating many moves ahead. Chess masters aspire to be Reti, and calculate only one move ahead.
As it is in chess, so it goes in logic games. The prep books and YouTube videos lead you to aspire to godlike powers of insight, able to unfold inferences at a glance. They lead you to think you should find the "truth" of the game, calculating inference upon inference until there is nothing left. Pure, shining insight amidst daunting complexity. If only you could master every inference, every problem would be simple.
I think you should want to be like Reti. See only what you need. Find only the inferences necessary to answer the questions. Look one move ahead, and find what is obvious and immediate. Would that not be much simpler? And yet it is so much more difficult. That one move, the right move, is much harder to find and takes vastly more skill.
Unfortunately, prep books and videos don't teach you to be Reti. They want you to be Alekhine. What is missing is that crucial step towards mastery: knowing how to find the right inferences, and only those. That is what they don't know how to do. So they throw acronyms at you, and they teach you kinds and types and strategies. But they don't teach you how to see only one move ahead. They don't show you how to find the right move.
Echo's sister, Kik, woke me up this morning to ask about diagrams. Early cat catches the mouse, sort of thing.
"Mmph Meowrf MEOWFFM Pbbbtt"
"Kik, what's in your mouth?"
"What the hell do you have in your mouth? Spit that out."
A moment later...
"A present! I brought you a present. It's a mouse. Now help me."
"That's not a mouse. It's a computer mouse. MY computer mouse, I might add."
"Whatever. Same thing. Help me."
"Help you with what?"
"Diagrams. Echo said you helped him, so I need you to help me. I think I get it, but I need you to take a look. I worked that problem about the scientists, and here's my diagram."
"Oh, you mean Logic Game #1, questions 1-5 from Test 42, Section 1" I said for totally unnecessary reasons having nothing to do with copyright or why I can't show you the specific problem without getting sued.
"Yea, nailed it. Good for you. Look..."
"Yeah, I see your problem" I said.
"But I followed your advice about diagrams! If there's a problem, that's on you."
"Well, you did and you didn't. Let me explain..."
The test allows approximately 8m45s per logic game. That's not a great deal of time, and so every second counts. Your diagram should use the least amount of effort, and take the least amount of time as possible. So never write out things like Botanist, Chemist, Zoologist. Use abbreviations or better yet, just use the letter with a circle around it. The circle tells you it's a category, not a variable.
I do like that you organized the variables by category. Very good thinking. But then you have "5" and "1 of each." That's too confusing. There's a simpler way to represent that only 5 variables are selected and at least one from each category. (See diagram below) But I really don't like how you diagrammed your rules.
"Why not?" Kik asked, "They're logically sound representations of the rules, aren't they?"
"Yes, they are. And they express exactly what the rule states, which is great. But they're not really usable at a glance. I'm going to have to do work to "convert" these rules into something that allows me to draw inferences and apply those rules to questions. And I'm lazy, like you ("Hey!"), and I don't want to do work -- also like you (<shrug>). Taking a little extra time to represent the rules in a logically usable and visually obvious way will save time later on. Here, look at my diagram.
"I don't get it," said Kik. "What's so great about this diagram compared to mine?"
Well let's start with speed. I didn't spend time writing out the categories. Circled letters, easy and fast. I didn't write out "1 of each" I just put dashes next to each category. Then I added two out to the side, as well. This tells me that there is one of each category, + 2 from any category. Not only that, but I represented those conditions in a visually obvious way. It's immediately clear how many variables are needed and of what type.
Now look at my rules. See, the LSAT wants to confuse you by stating the first rule in terms of Botanists and Zoologists. If you write B and Z, then you have to go back to your variables, look at who is what, then translate the rule. I skipped all of that extra work and just wrote the rule in terms of the variables themselves. After all, it's the impact on the variables that matters for answering the questions. So, my rule says "2 or more of FGH, then 1 of PQR." Yeah, I know the rule states "at most one of PQR" but that's just the LSAT trying to trick me. "At most one" logically means 0 or 1. But it CAN'T mean 0, can it? There must be one of each category, so "at most" 1 means just...one.
"But why," asked Kik "did you represent F --x-- K vertically and K --x-- M horizontally?"
Because that's how I structured my variables. See, F and K apply to different categories. And I stacked my categories. So, I stack that rule. Why? Because it visually matches how I've organized the problem, and so it is visually easier to reference. And I want it to be as easy and obvious as possible. But K and M are from the same category, so I diagram that rule horizontally.
Now, the "If M, then P + R" rule" is a conditional. But why express it as a conditional in logical form? Why not express it as it appears visually in the problem? So I use the curvy F symbol to indicate "If M." (that's my shorthand, and it works for me. use whatever you can draw with your kitty paws). It's important that this rule hinges on M being selected, and I want to represent that. But then I draw it stacked with PR beneath. Why? Because that's how I've organized my problem! At a glance, I can see the conditional. I've done the same with the two inferences at the bottom. There are more inferences, but I just want you to see how I diagrammed them. I diagrammed them to be visually obvious based on my organization of the problem. I don't have to piece the inference together. It's visually available.
"Yeah," said Kik "but I'm tired. I saw you ironing earlier. I think I'll go nap on your clothes."
My oldest cat, Echo, has been studying hard for the LSATs. He's taking it more seriously than the other two. He signed up for a course, but it didn't really help, and there were no treats like there are at home. He's working on logic games, but it's not going well. While taking a break on the cat tree, he said "You know, I feel like it's always just one or two inferences that I miss. If I could just get better at finding those inferences, I know I could do well!"
"Hmmmm," I said. "Ok, let me see your diagrams."
"Oh, diagrams aren't the trouble. I told you, INFERENCES! INFERENCES!"
Frustrated, he went to Mommy for hugs. Ungrateful hairball. So, I dug through his diagrams. I found this:
"Yeah," I told him, "the problem is NOT inferences. It's your diagrams."
How can you expect to find the inferences you need if you can't properly organize your information? The logic games give you an enormous amount of information, and the LSAT will test you on ALL of it. To succeed, you need to quickly, accurately, and completely represent that information in visual form.
You want to see at a glance all the information contained in the problem. Then you will be able to see inferences. This is especially important because the LSAT tries very hard to confuse you with the information it does give you, and it tries to make it hard to put that information in visually complete form. That's how mistakes...
...hey! put that down! Don't eat that!
That's how mistakes happen.
"Ok," Echo said, "so what are the features of a good diagram, Mr. SmartyPants?"
Well, this will get you started:
1) Organize your diagram around a central, STABLE variable. In Linear problems, for example, this means using the sequence they give you: days of the week, or docking bays, or order of deliveries. Your foundation should be built around the most stable variable.
2) Draw your diagram in a way that visually represents the logic of the problem! If you're organizing stores on different floors in a building, use a vertical diagram. If it's days of the week, use a horizontal diagram, for example.
3) Visually represent the rules as they would appear in your diagram! This makes it easier to understand how the rule functions and how it would fit in your diagram.
4) Always have a master diagram and put as much information in it as you can! If a rule says R is second, then put R in the second place. If it CAN go in your master diagram, put it there.
5) Diagram only what you are given. One of the ways the LSAT gets you to make mistakes is by getting you to make assumptions that seem natural but are not in the problem. For instance, the problem might say, "Six delivery trucks service three buildings K, L, and M, with each truck servicing at least one building." It is natural to assume that each building is served by at least one truck. But in the way it is worded, that is not necessarily true. All six trucks could service only one building and still meet the condition. If the problem said instead, "Six delivery trucks service three buildings, K, L, and M, with each truck servicing at least one building and each building is served by at least one truck," then yes, we know now that all buildings are served, and each truck serves at least one building.
"Got it? ---- hey, wake up!"
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