Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Basic Linear, Identify the Possibilities game.

Because Basic Linear games are generally easy to handle for most test takers, this was an
excellent way to begin the Logic Games section of the June 2007 LSAT.
The game scenario establishes that a product code uses five digits. From the first two
rules, we know that each digit is a unique number, from 0 to 4. Because there are no ties,
this is a Balanced game. The following linear scenario underpins the sequence:

0 1 2 3 45

june07_game_1_diagram_1.png

Notice that both the digits and their order in the product code are numerical variable sets.
This is no accident, as it was clearly meant as a potential source of confusion. Even
though each variable set has an inherent sense of order, it is clear that the order in which
the digits appear in the product code should be used as a base. If you find the numerical
nature of both sets potentially confusing, you can decide to forgo using numbers in your
base: with only five positions available, their numbers can be easily determined by sight.
After the first two rules, which establish the balanced nature of this game, the third rule is
critical: the second digit has a value exactly twice that of the first digit. For the sake of
clarity, we will represent the position numbers in brackets:

• (2) = 2*(1)

A quick look at the five values available (0, 1, 2, 3, 4) reveals that there are only two
ways to satisfy this rule:

june07_game_1_diagram_2.png

The fourth rule establishes that the value of the third digit is less than the value of the
fifth digit:

• (3) < (5)

The inequality established by the last rule will generate only a handful of possible
solutions. This is because, within each template, there are only three digits left to work
with (0, 2, and 4 in Template 1; 0, 1, and 3 in Template 2), and, consequently, only three
ways of ensuring that they are ordered in a manner consistent with the last rule:

june07_game_1_diagram_3.png

The decision to “dig deeper” into the two Templates and ultimately undertake a
Possibilities-driven approach results from several key factors. First, this is a Balanced
game with only five variables, which inherently limits the number of possible solutions.
Secondly, satisfying the third rule can only be done in one of two possible ways, each of
which fully determining the placement of two of these variables. Finally, the last rule
restricts the order of the remaining three variables. Thus, we arrive at the following final
setup for this game:

0 1 2 3 45

june07_game_1_diagram_1.png

(2) = 2*(1)
(3) < (5)

june07_game_1_diagram_3.png

[Morgan O'Donnell]

Can you please help me figure out how to set up this problem?

June 2007 LSAT, Game #1

*Also, #1 says the answer is A I have no idea how to set up the problem and how they got that answer.

Thanks!!

[Jon Denning]

Thanks for the question. Let's talk about the setup first, and then I'll address question 1.

This is an extremely restricted game that can be solved pretty easily by listing the various orders that are possible. What you'll eventually find is that only six different codes are possible based on the rules.

The first significant restriction is that the second digit is exactly twice as large as the first, meaning the first two numbers must be either 1-2, or 2-4 (no other pair works in the set of 01234). So we have two fundamental directions that the game can take, and when we combine that with the final rule saying the third digit is less than the fifth, only six orderings exist:

1-2-0-3-4
1-2-0-4-3
1-2-3-0-4
2-4-0-1-3
2-4-0-3-1
2-4-1-0-3

With those six you should be able to easily answer all of the questions.

For instance, here's the solution to question 1:

If the last digit is 1, only one order is possible: 2-4-0-3-1. So answer choice A is correct, since the first digit must be 2.

I hope that helps!

Jon

[saranash1]

How do you diagram the rules for this game?

[Lucas Moreau]

I would diagram it like this:

____ ____ ___ ____ ____
1D 2D 3D 4D 5D

The "D"s in this case standing for "digit", since having numbers for both the digit designators and the value of the digits themselves would be pointlessly confusing. You could also possibly use Roman numerals or A-E rather than #D.

As for the rules themselves, I would probably represent them with these:

(2D) = (1D)x2
(3D) > (5D)

Hope this helps!

[KwakuS]

Hello,

Thank you very much for this explanation of the game template. I notice that we have six different templates here, which seems to be a lot to solve before a game. At the same time, I noticed that having that those templates helped on question 5, which I missed. How do I determine whether or not making a template is too time-consuming? And also, if I did not have a template, how would I still solve this question in a timely manner?

Thanks,
Kwaku

[Rachael Wilkenfeld]

Kwaku, I think this game is incredibly tricky without at least the two main templates, even if you don't to the three subtemplates for each main template. Whenever you are deciding if you should do templates (or how far to template) you want to balance the time cost with the information gained. That is, will you have more information when you finish the templates that will help you in the game? How long will it take you to set up. In this case, all six templates are fairly quick. You really only have a few spots to fill in once you fill out the first two spots.

If you didn't have templates, I'd start with trying to prove each of the answer choices false. If you can come up with a scenario that works without the answer choice being true, it's eliminated.

Answer choice (A): 24013 works. Zero digits between the 0 and 1. Eliminated.
Answer choice (B): 24013 also works here. Two digits between the 2 and the 1. Eliminated.
Answer choice (C): 12043 is more than two digits between the 1 and the 3. Eliminated.
Answer choice (D): 24013 is more than two digits between the 2 and the 3. Eliminated.
Answer choice (E): This would require the 2 in first place and the 4 in the last place. Since the 2 in first requires the 4 in second, this cannot work. This has to be our correct answer.

This plug and chug sort of technique will work, but it is much more time consuming than just doing the templates up front, and comparing across the different templates.

Hope that helps!