This is an explanation of the third logic game from Section IV of LSAT Preptest 36, the December 2001 LSAT.
A group of six people ride a bus together. They are Gutierrez, Hoffman, Imamura, Kelly, Lapas, and Moore (G, H, I, K, L, M). The bus seats are numbered 1 through 3, from front to back. There are two rows and each row has two seats each (W, A).
Game Setup
This is a grouping game. We have three rows of two bus seats, and have to figure out where everybody sits.
This game is quite hard. You have to know all of the rules. Really, you have to know them: memorize them. Don’t try to understand this game if you don’t know the rules.
I’ve made a list of them below. There are only 5, so commit them to memory or write out the list yourself while trying this game. If one of my explanations says something must be true and you’re not sure why, it’s almost certainly because of one of the rules.
I find it easiest to draw this vertically. But if you drew a horizontal diagram, that can work too.
Here’s how I drew it:
The first rule is the most restrictive rule. G and H both sit in the aisles. G comes right before H.
There are only three aisle seats. So G and H can either go in 1 and 2, or 2 and 3.
Whenever a restrictive situation can only be drawn two ways, I always draw those two scenarios. I find it is very useful to help me think through the diagram.
These will also serve as guides when we have to make sketches for later questions.
We could make exhaustive scenarios for the next four rules, but there are too many to be useful.
Instead, I recommend making a numbered list of the last four rules, memorizing them, and/or referring back to the list quickly as needed. This game centers on the rules.
The next rule is that if M is in an aisle seat then L is in the same row as H.
We know that G is always above H. So we can expand on this rule by including that.
The third rule is that if G and K are in the same row then M is behind I.
I placed H under G, because G is always over H. This rule actually lets us figure out quite a lot, but I’ve put that in a separate section later.
The fourth rule is that if K is in a window then M is in row 3.
If M is in the aisles, then K must be in a window seat (because only three variables can fit in the aisles.)
So if M is in an aisle seat then K will force M to be in seat 3.
The final rule tells us that if K is in 3 then Imamura is in 1.
Scenarios
This isn’t essential. I’m adding this section to show you how you could build scenarios to help you on this game.
I didn’t use these on the questions, but drawing them helped me get a better intuition for the game.
When you have a conditional rule, it’s good to think through all of its implications. Consider the third rule. If G and K are in the same row, M, is behind I:
That’s pretty restrictive. It covers five variables. We can only fit three variables in the window or aisle columns.
There’s no room for I to be over M in the aisle seats, because G and H are already there. There are four variables but only three spots.
So they have to go in the window seats. K has to go above them. It’s the only way to fit all three and still have space for H.
The only other way to place K and IM would be to put K in 3 and IM in 1-2. But then G would be in 3 and there would be no space to put H below.
By default, L will go in the bottom of the aisle seats:
So if K and G are in the same row, there’s only one way to place the variables.
Therefore we can make a further deduction is that K and G can’t go together unless they are in the first row. We can add this to the main diagram:
There is one more scenario worth drawing. We should figure out what happens if M is in an aisle seat, since there are many restrictions when that happens.
If M is in an aisle seat, then K, L and I are in window seats. If K is in a window seat, M goes in seat 3:
If M is in the aisles, H and L are on the same row. This fills row 2:
That leaves K and Imamura to be placed in rows 1 and 3. It turns out we can’t place K in row 1. Why? Then K would be beside G. We saw that scenario earlier: if K is beside G, M has to be directly below Imamura.
So K must go in 3 and Imamura in 1:
This scenario involved almost every rule. So if you weren’t sure how to do it, go back and review the rules, or try drawing it yourself. It’s a useful exercise to be sure you’re applying the rules correctly.
As I said, you don’t need these scenarios to get this game correct. But drawing them correctly will help your diagramming skills.
Solving A Rules Based Game
Some of my diagrams for the individual questions may seem mysterious, so I want to explain what I’m doing.
Questions 15-18 are all “local rule” questions. The game gives you a new rule, and you can combine this rule with the existing rules to make new deductions.
Take question 15 for example. The question says that L and K are in window seats.
If you properly memorized the rules, you’ll notice a rule is triggered by this new condition. If you didn’t memorize the rules, look at the list to the right.
If K is in a window seat, M is in row 3.
This simple deduction lets us solve everything. There are only two places to put M in row 3: window or aisle.
From there, you can continue to make deductions until everything is solved. See question 15 for the full walkthrough.
In general, the process should be:
- Identify local rule
- See which regular rules it affects.
- Make a deduction
- Continue combining those deductions with the regular rules, until you’re done.
- Check if you found the answer.
I encourage you to try this process for each question before looking at my explanations.
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