Ordering
games might be the easiest of the four main game types, which
is good for you since they are also the most common type of game
found on the LSAT . Ordering games require you to organize the
elements or subjects of the game into either a spatial or sequential
order. We will begin this section by describing the types of
ordering games that you might encounter on the LSAT . We will
then apply the basic game solving strategy that we outlined in
the first part of this chapter to an ordering game. We will create
a diagram on which we will summarize the given information from
the game and use the diagrams to solve some game problems.
Spatial Ordering
There
are a few different ways in which Logic Games may require you
to arrange the elements of the game spatially. A problem might
require you to arrange subjects linearly, from front to back,
up to down, or from left to right. Imagine a group of people
standing in line for the theater. Who is second from last in
line? How many people are behind Tamas but in front of Christina?
Or perhaps you will be asked the order of several books on a
shelf. Is the art book next to the gardening book or the photography
book? How many books can be to the left of the philosophy book
if the drama criticism is not at either end of the shelf? In
addition to linear games, there may also be games that require
a novel spatial arrangement, such as the seating arrangement
for a dinner party of seven people at a round table.
Sequential ordering
Games
can also require you to arrange the elements of the game temporally,
that is, in a time sequence. For example, imagine that seven
people need to give speeches at the council meeting. If Barbara
needs to give her speech after Charles gives his, but before
Miriam gives hers, what is the fewest number of people that must
follow Barbara?
Ordering by characteristic
The
final basic type of ordering game is one that requires you to
arrange the elements of the game according to some other characteristic.
Now, there is a separate type of game called characteristic/attribute
games (and a separate section describing these games later in
this chapter), but we are talking about a different kind of problems
here. These kind of problems, although involving a characteristic,
are actually ordering games in that they ask you to order elements
based on some characteristic for which there is an obvious sequence
or order. An example of this kind of question would be if you
are asked to arrange a group of boys by height, from shortest
to tallest, or to create a list of countries arranged from smallest
to largest landmass.
Solving
Although
on the surface these three game subtypes may seem different,
they can be solved similarly. What they all have in common is
the relatively straightforward nature of the relationships between
the game's elements and the simple diagram that is needed to
represent these relationships.
Like
the other games you will encounter on the LSAT , we will start
by applying the step-by-step method we outlined for you in the
last section. Then, we will create a diagram on which we will
summarize the given information.
Let's start with a relatively
easy game:
Sample Game One
At a state fair, the prize-winning
cows of six different breeds, Ayrshire, Brown Swiss, Guernsey,
Jersey, Holstein, and Simmental, are to be displayed in the central
stock pavilion. There are six stalls numbered 1 to 6 from left
to right. Each cow will be housed in its own stall.
The Jersey is not in either the
leftmost or rightmost stall.
There are exactly two cows between
the Holstein and the Simmental.
The Brown Swiss and Jersey are
next to each other.
The Guernsey is in stall three.
Okay, after we have read through
the game set-up and the conditions, let's start by making a roster.
In this case, the elements are the six different cows.
Roster: A, B, G, J, H, S
Next, we need to summarize the
conditions of the game. It is very important to do this carefully!
The precise reading of the game conditions and the translation
of these conditions into concise, symbolic statements are absolutely
critical skills required for a good score on the analytical section.
To demonstrate, we will go through each condition and its translation
into concise, symbolic form.
The first statement tells us
that the Jersey is not in either the leftmost or rightmost stall.
This can be translated into:
J ? 1, J ? 6
There are exactly two cows between
the Holstein and Simmental can be written as:
H _ _ S or S _ _ H (the dashes
represent additional cows)
Why do we write two statements?
We do not yet know which cow, the Holstein or the Simmental is
closest to the left. We only know their positions relative to
each other, not their exact locations. When you have a flexible
statement like this, you should always write out both possibilities.
The next statement tells us that
the Brown Swiss and Jersey are next to each other. We can represent
this as:
BJ or JB
The statement that the Guernsey
is in stall three can be represented as:
G = 3
Once we have summarized the rules,
let's think about what kind of diagram would be most helpful.
What sort of problem are we being asked to solve? This is a linear
ordering game, as we are being asked to arrange these six cows
from left to right. This situation can best be represented by
six dashes, one for each stall.
Now, let's fill in the information
that follows from the rules, starting with the fixed condition,
G = 3.
What other information can we add to our diagram? Well, we are
told that J cannot be in 1 or 6, so we could add that informatino
also, in the form of ^J in stalls 1 and 6.
Now, remember we told you that
often you are able to garner additional information by considering
conditions together. You are also often able to make deductions
when trying to fit the conditions to the diagram. We know that
H _ _ S or S _ _ H. If we look at our diagram, how many ways
can we fit this condition into the available open stalls? If
we put H in stall 1, then S would have to be in stall 4 (or S
in stall 1 and H in stall 4). We can represent the idea that
either H or S can be in stall 1 and the other in stall 4 as in
the following diagram.
This would leave only stalls 5 and 6 open for the two cows that
need to be next to each other, the Brown Swiss and Jersey. Since
we also know that the Jersey cannot be in stall 6, we can place
these cows with certainty in the following diagram.
Is there any other way we can fit the H _ _ S or S _ _ H condition
into the diagram? Stall 3 is already taken, but stalls 2 and
5 would be the correct distance apart. Let's see what happens
if we try to fit the H and S cows into spaces 2 and 5.
Now when we try to fit the next condition, BJ or JB, we see that
there are not two adjacent spaces available. Therefore, we can
eliminate this diagram.
Now that we have the diagram,
let's look at a sample question.
1. If the Ayrshire cow is next
to the Simmental cow, which of the following cannot be true:
(A) The Jersey cow is next to
the Holstein.
(B) The Guernsey is next to the Ayrshire.
(C) The Ayrshire cow is in stall two.
(D) The Simmental cow is in stall four.
(E) The Holstein is in stall four.
To solve this, let's look again
at our diagram.
We are told in this question
that the Ayrshire cow is next to the Simmental cow. Acording
to our diagram, the only stall available for this cow is stall
2. If we place the Ayrshire cow in stall 2, then in order to
meed the new condition that the Ayrshire cow is next to the Simmental
cow, we must place the Simmental cow in stall 1, which makes
the Holstein in stall 4. Now our diagram looks like this:
Now that our diagram is completely filled in, the question is
easy to answer. Since it is asking which statement cannot be
tru, we must go through each one and check it against our diagram.
Is the Jerset cow next to the Holstein? Yes. Is the Guernsey
next to the Ayrshire? Yes. Is the Ayrshire cow in stall two?
Yes,. Is the Simmental cow in stall four? No, it is in stall
one. This statement is not true, and therefore the correct answer.
To be sure, we can check the last choice, is the Holstein in
stall four? Yes.
Now, will we always be able to
fill in all of the blanks in our diagram? Of course not. In fact,
the more complicated the game, the fewer fixed elements there
will be. What this means is that often you will require multiple
diagrams, or diagrams that have multiple options for certain
positions.
Let's try another ordering game,
this one a little more complicated:
Sample Game Two
Veebee's department store occupies
five of the six floors in a building. On the remaining floor
is a restaurant. The floors are numbered one through six, with
the first floor at the bottom and the sixth at the top. Veebee's
has four departments: housewares, kids, furniture and clothing.
Each department occupies a separate floor except the clothing
department, which occupies two adjacent floors.
The kids department cannot be
located on a floor immediately above or immediately below a floor
occupied by the clothing department.
The housewares department is
either on the floor immediately above or immediately below the
furniture department.
We can see immediately that this
ordering game has fewer conditions than the last one. Does fewer
conditions mean the game is more simple? No, instead it often
means that there will be more possibilities to be worked through
for each question.
First let's create the roster,
in this case the different departments.
Roster: H, K, F, C1, C2, R.
Note that in this case, one of
the elements (clothing) takes up two spaces (two floors). To
help us remember that when designing our diagram, we can call
these C1 and C2.
What kind of diagram should we
use? This is a linear ordering game, but this time instead of
arranging the elements from left to right, we need to arrange
them vertically, like the floors of a building. (It is always
a good idea to make your diagrams as representative as possible
of the type of arrangement you are asked to make, that is to
say, draw a horizontal line if you are arranging things in a
line, draw a vertical line if arranging things on top of each
other, etc. )
Now, let's create a vertical
set of six lines to represent the floors, and to the right of
this diagram, we can represent the conditions. We are not able
to put the conditions onto the actual diagram at this point,
because we do not have enough information. When we are given
more information in the questions, we will then fit the conditions
into the diagram, but for now, we will start with this:
Let's try the questions.
Question One:
If the clothing department occupies
the third floor, and the restaurant is not on the second floor,
which of the following must be true?
(A) The kids department is on
the sixth floor.
(B) The fourth floor is occupied by the clothing department.
(C) Furniture and housewares are on the top two floors.
(D) The kids department is on the first floor.
(E) The restaurant is on the fifth floor.
Okay, in this question we are
given more information to help us to create our diagram. If the
clothing department is on the third floor, what else do we know?
Well, the clothing department occupies two adjacent floors, so
that means either the second or fourth floor must also be clothing.
Since we do not know which is correct, we must explore both possibilities.
We are also told the restaurant is not on the second floor. Let's
try to represent this information with two diagrams.
Now we have two diagrams that
include the information from the question. We have additional
information to consider, however. We know that the housewares
and furniture departments are on adjacent floors. How can we
fit this into our two diagrams? When we try to place these two
floors on the first diagram, we can see that there are two possibilities
for these two departments: the fourth and fifth floors or the
fifth and sixth floors. For the second diagram, there is only
one possible location of the two floors, so the end result is
three diagrams (two derived from the first, one from the second).
(Note: remember that we do not know if housewares or furniture
is located on the higher floor, thus if we wanted to, we could
draw the two possible arrangements for each, instead of H/F and
F/H as we have depicted. This would give us six diagrams! A good
rule of thumb is to approach the question with the simplest diagram
(or diagrams) and then see if you can answer the question. If
not, you may want to draw out the other possibilities.)
Now let's try to answer the question
by going through each of the answer choices. ChoiceA states that
the kids department must be on the sixth floor. First look at
the first diagram. There are two unassigned floors, the first
and the sixth. The first one we have already noted cannot be
the kids department, so the sixth must have the kids department.
What about the second diagram? There is no space available for
the kids department! So we can eliminate this diagram as a possible
arrangement. Let's look at the third diagram. In this one, the
only unassigned floors are the fifth and the sixth, and the fifth
we have already labeled as not able to be occupied by the kids
department. Therefore for this arrangement also, the kids department
is located on the sixth floor, so this is the correct answer.
To be sure, let's also go through
the other choices. Choice B states that the fourth floor is occupied
by the clothing department. If we look at our diagrams, in the
first one, this is not true, the clothing departments are on
the third and second floors. It is true for our third diagram,
but since we are asked for which condition must be true, we can
eliminate choice B.
Choice C states that furniture
and housewares must be on the top two floors. We can see from
our diagrams that this cannot be true, instead, the kids department
must be on the top floor. Choice D says that the kids department
is on the first floor. We have already established that the kids
department is on the sixth, so we can eliminate this one. Choice
E places the restaurant on the fifth floor. While this would
work for our third diagram, it does not work for the first diagram,
therefore this choice too can be eliminated.
Let's try another question for
the same game.
Question Two:
Which of the following, from
first to sixth, represents a possible arrangement of the departments
and restaurant?
(A) Furniture, housewares, restaurant,
kids, clothing, clothing
(B) Furniture, kids, housewares, restaurant, clothing, clothing
(C) Clothing, clothing, furniture, housewares, kids, restaurant
(D) Restaurant, clothing, housewares, furniture, kids, clothing
(E) Restaurant, clothing, clothing,, furniture, kids, housewares
To
answer this question, which diagrams do we use? It is very important
to remember when starting a new question to not necessarily use
the last diagram you made. Remember that we added to our diagrams
the additional conditions that were given in the question itself,
rather than in the initial set-up or the original list of conditions.
These do not carry over to the next question. Instead, go back
to the original diagram.
Are
there additional conditions we can use to fill in more information?
No. We must rely only on the information we already have. Let's
work through the answer choices considering the three rules we
have: the two clothing floors are adjacent, housewares and furniture
are adjacent, kids not immediately below or above a clothing
floor. Choice A violates the rule about the kids department.
Choice B violates the condition that the furniture and housewares
departments should be on adjacent floors. Choice C seems to be
valid, but let's make sure by checking the last two choices as
well. Choice D violates the two clothing floors being adjacent,
and choice E violates the housewares and furniture rule. Therefore
choice C is the correct answer.
Summary of Strategy for Ordering
games
The
basic strategy outlined in the first section of this chapter
should be followed for ordering games. Once you have read the
premise of the game and the conditions, create the roster and
symbolize the conditions. Then, figure out what kind of diagram
is necessary to best represent the arrangement of elements in
the game and draw this. Write the conditions for the game to
the side. Next, any conditions that are fixed can be put into
the diagram. Look over the conditions again to see if any new
information can be deduced when considered together with your
diagram. Next, proceed to the question and add any new information
to your diagram. If there are more than one possible arrangement,
draw the different variations out. Finally, read through the
answer choices, compare them to your diagram, and answer the
question!
1: Ordering Games
2: Characteristic Games
3: Grouping Games
4: Network Games
5: Non Linear Spatial Games
6: Map Games
Continue to:
II.
GAME TYPE 2: CHARACTERISTIC GAMES
