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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.

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.

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

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