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Get the Specs: Tackling the Rules
Get the Specs: Tackling the Rules
So now we know what kind of game we’re dealing with and who the characters are and what you’ll be doing with them. Now it’s time to tackle the rules, which specifically spell out how the characters interact. The rules lay down the specs that you’ll need to follow when tackling each question.
Keep in mind that the rules apply to all of the questions in the question set, except for rare questions that specifically add a new rule or omit or modify an existing rule. In those cases, the rule change applies only to that particular question.
Some rules are complicated, and these are the ones you’ll need to spend the most time learning how to handle. However, don’t overlook the conventional rules that appear in many games. While these are fairly straightforward, you still need to quickly recognize their implications. Many games are ruined by careless misinterpretations of what appear on the surface to be simple rules, so it’s worth taking a look at these before tackling the tough stuff.
Conventional Rules
Direct Positive
A Direct Positive rule explicitly tells you something that must be the case. Here are examples of Direct Positive rules for each of the game types discussed above, beginning with the Ordering game.
Art Lectures: Ordering

Seven works of art—P, Q, R, S, T, V, and W—will be exhibited at a local gallery opening. A short lecture will be delivered by the creator of each work during the gallery opening. No two lectures will be delivered at the same time. The sequence of lectures must satisfy the following requirements:

Rule: The lecture on artwork Q will be delivered fifth.

Here you’d go right ahead and place a Q under number 5 in your initial sketch. The logical implications are that Q cannot go anywhere else, and no other artwork can take space 5.
P Q R S T V W
1
2
3
4
5
6
7
Q
In Ordering games, a special case of this rule can occur when a character is directly assigned to either end of the sequence, since that creates additional implications. For example, if a rule stated that the lecture on artwork S must be delivered first, then the additional implication is that no lecture precedes the lecture on S, and that S’s lecture does not come after any others. Conversely, if S’s lecture was assigned to space 7, no lecture can come after S’s, and S’s lecture cannot come before any others. Note also that a Direct Positive rule can be stated in the negative, for example: “No lecture is delivered later in the week than the lecture on artwork K.” Different wording, same result. We know exactly in this case where lecture K is—last, which means seventh. Any rule that allows you to write a character directly into your blueprint is a Direct Positive.
Let’s now see what a Direct Positive would look like in the context of our Choosing game.
Maggie’s Courses: Choosing

Maggie must select exactly three introductory courses for the upcoming semester. The available introductory courses are biology, communications, English, French, history, literature, and philosophy. Her selection must accord with the following conditions:

Rule: Maggie will select French.

In this case you’d go right ahead and put an F into one of the three slots in your blueprint. The logical implication is that only two spots remain to be filled.
B C E F H L P
__F___
_____
_____
Let’s try the same with our Placing game.
Economic Seminars: Placing

The participants of two economic seminars, one on free trade and one on venture capital, are to be assigned from among six company employees—Jobson, King, Lee, Manute, Nora, and Orson. King and Nora are vice presidents; the rest of the employees are middle managers. Each employee must participate in at least one seminar. The following rules govern the assignment of employees to seminars:

Rule: Lee will participate in the seminar on free trade.

This tells you to place an L in the free trade column. Nothing in the introduction to this game suggests that employees must only participate in one seminar, so we can’t tell yet whether Lee participates in venture capital as well. But we do know that at least one middle manager participates in free trade, since Lee is defined as such in the intro.
VP
MM
KN
JLMO
FT
VC
L
Now let’s wrap up Direct Positives with our Linking scenario.
Birthday Party: Linking

Six children—Edel, Francie, Gillian, Holly, James, and Kayli—attend a birthday party. Three of the children are in nursery school, two are in first grade, and one is in second grade. Each child eats either pizza or a sandwich at the party. No child eats both kinds of food. The following must obtain:

Rule: Gillian eats a sandwich.

If you were keeping track of the information using a table, you’d place a check in the box intersecting G and S. If you’re using a list instead, you’d simply write an S above or below G in your cast of characters. Since the game stipulates that each child eats either pizza or a sandwich, the implication of this rule is that Gillian does not eat pizza.
E
F
G
H
J
K
S
Direct Positive rules and their implications are fairly simple, but they are often used as the starting point for longer chains of reasoning. Don’t overlook them or underestimate their importance.
Direct Negative
A Direct Negative rule explicitly tells you something that CANNOT be the case. Here are examples of Direct Negatives for each of the major game types, based on the same game introductions utilized above.
Art Lectures: Ordering

Seven works of art—P, Q, R, S, T, V, and W—will be exhibited at a local gallery opening. A short lecture will be delivered by the creator of each work during the gallery opening. No two lectures will be delivered at the same time. The sequence of lectures must satisfy the following requirements:

Rule: The lecture on artwork Q will not be delivered fifth.

no Q
1
2
3
4
5
6
7
Writing “no Q” above the fifth slot in your blueprint for this Ordering game would suffice to represent this rule. This tells us that Q must be somewhere else. Sometimes the negative will include multiple spots in the sequence. For example: “The lecture on artwork Q will not be delivered second or fifth.”
Moving on, you generally won’t see a Direct Negative in a Choosing game, since there would be no reason to include a character in the game that can never be chosen. For example, in the game in which Maggie is to choose three of the seven available courses, it would make no sense to see a rule that says “Maggie will not choose literature.” If she can never choose it, why include literature in the first place? Direct Negative rules do apply perfectly well, however, to Placing games.
Economic Seminars: Placing

The participants of two economic seminars, one on free trade and one on venture capital, are to be assigned from among six company employees—Jobson, King, Lee, Manute, Nora, and Orson. King and Nora are vice presidents; the rest of the employees are middle managers. Each employee must participate in at least one seminar. The following rules govern the assignment of employees to seminars:

Rule: Lee will not participate in the seminar on free trade.

Since each employee must participate in at least one seminar, this rule allows you to deduce that Lee must participate in the venture capital seminar.
Turn negatives into positives whenever possible! When told what CANNOT be true of a particular character, see if you can bounce that information off the other game parameters to deduce something that MUST be true.
You may come across Direct Negative rules in Linking games as well.
Birthday Party: Linking

Six children—Edel, Francie, Gillian, Holly, James, and Kayli—attend a birthday party. Three of the children are in nursery school, two are in first grade, and one is in second grade. Each child eats either pizza or a sandwich at the party. No child eats both kinds of food. The following must obtain:

Rule: Gillian does not eat a sandwich.

Following the advice to turn negatives into positives, you’d deduce that Gillian must therefore eat pizza, since sandwich and pizza are her only options.
Again, these conventional rules aren’t rocket science, but if you bollix one up, you’ll be in for a tough time. So it’s definitely worth thinking through these basic implications before tackling the tougher stuff. We continue our discussion of conventional rules with a slightly more complex variety: rules that impose relationships between characters.
Positive Relationship
A Positive Relationship rule creates a positive link between two characters or aspects in the game. Here are examples of positive relationships for each of the major game types, again beginning with Ordering.
Art Lectures: Ordering

Seven works of art—P, Q, R, S, T, V, and W—will be exhibited at a local gallery opening. A short lecture will be delivered by the creator of each work during the gallery opening. No two lectures will be delivered at the same time. The sequence of lectures must satisfy the following requirements:

Rule: The lecture on artwork Q will be delivered immediately before or immediately after the lecture on artwork V.

This rule creates a “cluster” out of characters Q and V. The word “immediately” tells us that these two characters must be right next to each other somewhere in the sequence, although we don’t yet know in what order. “QV or VQ” is an effective way to shorthand this common Ordering rule. Note that we also don’t know where in the ordering this cluster will appear (first and second? fourth and fifth? sixth and seventh? etc.), but the fact that it takes up a definite two-slot portion of real estate will certainly come into play in your solution to many questions.
Clusters can consist of two, three, and even four characters. Many games test your ability to space out such clusters among the other characters without violating other rules.
Another common Positive Relationship Ordering rule specifies the exact number of spaces between two characters. For example:

Rule: Exactly two lectures will be delivered between the lecture on artwork Q and the lecture on artwork V.

Here’s how you can shorthand this:
Q __ __ V
V __ __ Q
Yet another common Positive Relationship Ordering rule forces characters before or after other characters but does not specify the distance between them. Check out an example on the next page.

Rule: The lecture on artwork Q will come after the lecture on artwork V.

In this case, we can deduce for sure that Q can’t be first and V can’t be last. Beyond that, we don’t know how many lectures come between them. The rule is satisfied as long as V is before Q. Using “. . .” is a good way to represent this:
V . . . Q
As we’ll see later on, it’s possible to form helpful deductions when more than one rule like this shares a common character.
Choosing games are not good candidates for simple Positive Relationship rules. We’ll see how the characters in Choosing games interact positively and negatively when we get to Conditional rules. But let’s move on to Placing games.
Economic Seminars: Placing

The participants of two economic seminars, one on free trade and one on venture capital, are to be assigned from among six company employees—Jobson, King, Lee, Manute, Nora, and Orson. King and Nora are Vice Presidents; the rest of the employees are middle managers. Each employee must participate in at least one seminar. The following rules govern the assignment of employees to seminars:

Rule: Jobson and Manute will each attend exactly one seminar and will attend that seminar together.

This tells us that J and M will be together at exactly one seminar, but it does not tell us which one. However, as soon as we see Jobson somewhere, we’d have to place Manute there too, and vice versa. In addition, this implies that J and M cannot attend the other seminar.
Now let’s check out this kind of rule in our Linking scenario.
Birthday Party: Linking

Six children—Edel, Francie, Gillian, Holly, James, and Kayli—attend a birthday party. Three of the children are in nursery school, two are in first grade, and one is in second grade. Each child eats either pizza or a sandwich at the party. No child eats both kinds of food. The following must obtain:

Rule: At least one first grader eats pizza.

There are two first graders, and this rule sets up a positive relationship between one of those first graders and pizza. Note that this leaves open the possibility that the other first grader eats pizza too. If the test makers wished to close off that possibility, they would have written “Exactly one first grader eats pizza.”
Much as in Logical Reasoning and Reading Comprehension, precision of language is a key component to Logic Games. Failing to grasp the difference between “at least” and “exactly” spells doom in this section.
By now you probably sense that where there are positives, there are likely to be negatives, and you wouldn’t be mistaken in that assumption. Which brings us to our next category . . .
Negative Relationship
A Negative Relationship rule creates a negative link between two characters or aspects in the game. As always, this is best understood in the context of examples, so here goes.
Art Lectures: Ordering

Seven works of art—P, Q, R, S, T, V, and W—will be exhibited at a local gallery opening. A short lecture will be delivered by the creator of each work during the gallery opening. No two lectures will be delivered at the same time. The sequence of lectures must satisfy the following requirements:

Rule: The lecture on artwork Q will not be delivered immediately before or immediately after the lecture on artwork V.

This rule creates the opposite of a cluster: space between characters. “No QV or VQ” would suffice to shorthand this rule and would serve as a quick reminder that these two characters will never occupy adjacent spaces. This means that as soon as we know where one of them is, we know one or two places where the other character CANNOT be: one spot off limits if the known character appears at either end of the ordering and two spots off limits if the known character appears in the interior of the ordering, with a space to the right and left of it. Knowing the location of one of the characters could therefore be used to determine where that other character could be, or at least to narrow down the possibilities.
Characters in Choosing games may be characterized by Negative Relationships, such as in the following scenario.
Maggie’s Courses: Choosing

Maggie must select exactly three introductory courses for the upcoming semester. The available introductory courses are biology, communications, English, French, history, literature, and philosophy. Her selection must accord with the following conditions:

Rule: Maggie will not select French if she selects English.

Order doesn’t matter in a Choosing game, so we can simply shorthand this rule as “No FE.” The implications are that if she chooses French, she can’t choose English, and if she chooses English, she can’t choose French. It is possible, however, for her to reject both.
A key to Logic Games is understanding not just what the rules forbid but also what they allow.
It’s time to get negative about Placing. Consider the following.
Economic Seminars: Placing

The participants of two economic seminars, one on free trade and one on venture capital, are to be assigned from among six company employees—Jobson, King, Lee, Manute, Nora, and Orson. King and Nora are vice presidents; the rest of the employees are middle managers. Each employee must participate in at least one seminar. The following rules govern the assignment of employees to seminars:

Rule: Jobson and Manute will not attend a seminar together.

This tells us that anywhere J is, M cannot be, and vice versa. Since J and M must both appear somewhere, we can infer from this rule that each one attends exactly one seminar. That’s because if either attended both, they would have to be together in at least one of them, in opposition to the rule. Note that we can’t tell yet which employee attends which seminar. “No JM” will serves as a good enough reminder until we receive more information that allows us to place them definitively.
Let’s bring this rule category to a close with our final game type, Linking.
Birthday Party: Linking

Six children—Edel, Francie, Gillian, Holly, James, and Kayli—attend a birthday party. Three of the children are in nursery school, two are in first grade, and one is in second grade. Each child eats either pizza or a sandwich at the party. No child eats both kinds of food. The following must obtain:

Rule: No first grader eats pizza.

In a simple Linking game like this one, a Negative Relationship rule translates easily into a Positive rule. Since there are only two food choices, eliminating pizza as an option for first graders means that both first graders must eat sandwiches. In more complicated games, negative rules still can be turned into positive statements, even if it doesn’t result in a definite deduction. For example, if the food choices included macaroni, then the implication of this negative rule would be that each first grader must eat either a sandwich or macaroni.
It bears repeating: Whether dealing with a Direct Negative rule, Negative Relationship rule, or any other negative element of the more complex rules to come, always try to turn negatives into positives. Negatives are nice, if that’s all you can get. But when you can turn negatives into positives, that’s when the games break wide open. Knowing what is is more powerful than knowing what isn’t.
Number Rules
It’s very important to understand the numbers that govern each game. Sometimes numerical information is included in the game introduction, while other times it’s provided in the rules themselves. Let’s work through some typical examples of Number rules, again beginning with the Ordering game type.
Art Lectures: Ordering

Seven works of art—P, Q, R, S, T, V, and W—will be exhibited at a local gallery opening. A short lecture will be delivered by the creator of each work during the gallery opening. No two lectures will be delivered at the same time. The sequence of lectures must satisfy the following requirements:

Rule: At least four lectures are delivered after the lecture delivered on artwork Q.

With seven lectures total, you’d be expected to take this to its logical conclusion: Q’s lecture must be delivered first, second, or third. Any later would violate the rule. Again, notice how they tell you one thing but fully expect you to derive something more concrete from it.
Now take a look at how numbers may influence a Choosing game.
Maggie’s Courses: Choosing

Maggie must select exactly three introductory courses for the upcoming semester. The available introductory courses are biology, communications, English, French, history, literature, and philosophy. Her selection must accord with the following conditions:

Here very important numerical information is provided in the first sentence of the introduction itself, strictly defining the parameters of the game. Maggie must choose exactly three of the available seven courses.
Numbers often come into play in Placing games too.
Economic Seminars: Placing

The participants of two economic seminars, one on free trade and one on venture capital, are to be assigned from among six company employees—Jobson, King, Lee, Manute, Nora, and Orson. King and Nora are vice presidents; the rest of the employees are middle managers. Each employee must participate in at least one seminar. The following rules govern the assignment of employees to seminars:

Rule: Exactly three middle managers will participate in the venture capital seminar.

Very helpful information, since there are exactly four middle managers total in the game. Since Jobson, Lee, Manute, and Orson are the only middle managers, this rule tells us that three of them will participate in the venture capital seminar while the other must sit in on free trade. No doubt some of the questions will play off this breakdown, which you’ll need to manipulate in various ways depending on information presented in the other rules or the question stems.
Let’s see an example of how numbers may influence a Linking game.
Birthday Party: Linking

Six children—Edel, Francie, Gillian, Holly, James, and Kayli—attend a birthday party. Three of the children are in nursery school, two are in first grade, and one is in second grade. Each child eats either pizza or a sandwich at the party. No child eats both kinds of food. The following must obtain:

Rule: There are more second graders who eat pizza than first graders who eat pizza.

The birthday party game contains numerical information right in the introduction which, when combined with this number rule, yields a valuable Game Breaker (something we’ll discuss in greater depth when we get to Step 3). There is only one second grader in the game, so the only way that more second graders than first graders can eat pizza is if no first graders eat pizza. So should you write down “No first grade pizza”? No! Since there’s only pizza and sandwiches in this game, “no pizza” means “sandwiches.” So the full implication of this number rule is that the lone second grader must eat pizza, while both first graders eat sandwiches.
Always drive the information as far as it will go! People who do this usually do well on Logic Games, for the simple reason that this is one of the major things that’s tested: the ability to recognize proper logical implications.
Of course, Number rules come in all shapes and sizes, and you’ll be seeing plenty of them in the pages ahead. Now, however, it’s time to turn our attention to the more complicated rules standing between you and Logic Games success.
While you’re expected to instinctively understand the types of conventional rules discussed to this point, there are other kinds of rules that require a bit more brainpower. Let’s jump right in with Positive Conditionals.
Complex Rules
Positive Conditional
Positive Conditional rules consist of if/then statements and statements that can be translated into if/then statements. These tend to give many test takers trouble. Let’s see how these work, beginning with the same Ordering game we’ve been using throughout.
Art lectures: Ordering

Seven works of art—P, Q, R, S, T, V, and W—will be exhibited at a local gallery opening. A short lecture will be delivered by the creator of each work during the gallery opening. No two lectures will be delivered at the same time. The sequence of lectures must satisfy the following requirements:

Rule: If the lecture on artwork Q is third, then the lecture on artwork V is fifth.

In our discussion of if/then statements in the Logical Reasoning chapter, we invoked a technique called reverse and negate (referred to by some as the “contrapositive”). Here’s how it works:
The statement “If X, then Y” is logically equivalent to the statement “If NOT Y, then NOT X.” We first reverse the order of the characters in the statement, and then we negate both terms to form a statement that means the same as the original.
Try it out in the case of the Ordering rule above: First reverse the terms to get “If V fifth, then Q third.” Then (and make sure to do this second step!), negate both to get “If V is NOT fifth, then Q is NOT third.” Is that logically equivalent to the original? You bet—for the simple reason that Q third requires V fifth. If V is not fifth, yet Q is still third, then we’d be in violation of the rule. Here’s how you might shorthand this on the page:
If Q3, then V5
If V NOT 5, then Q NOT 3
Now let’s consider a rule that’s a bit more complicated.

Rule: If the lecture on artwork Q is third, then the lecture on artwork V is fifth and the lecture on artwork S is seventh.

In this case, if Q is third, then two specific things must happen. What would violate this rule? If either thing didn’t happen while Q was third—that is, if V is NOT fifth and/or S is NOT seventh. Either occurrence, by itself, is enough to violate the rule. So here’s how we could shorthand both the rule and its logical implications:
If Q3, then V5 and S7
If V NOT 5 or S NOT 7, then Q NOT 3
Consider one last variation on this theme:

Rule: If the lecture on artwork R is second and the lecture on artwork T is fourth, then the lecture on artwork W is fifth.

In this case, a combination of two conditions causes a third event to occur. This means that if this third event does not occur, then the original combination cannot occur either. That means that either part of the combination could happen without the other, or that neither part could occur, which is fine too. The only thing that couldn’t happen is both occurring if the third event is missing. We can note this as follows:
If R2 and T4, then W5
If W NOT 5, then NOT BOTH R2 and T4
We can apply the same type of reasoning to our Choosing game scenario.
Maggie’s Courses: Choosing

Maggie must select exactly three introductory courses for the upcoming semester. The available introductory courses are biology, communications, English, French, history, literature, and philosophy. Her selection must accord with the following conditions:

Rule: Biology is included in any group of courses selected that includes history.

An interesting thing to note from this rule is that not every conditional statement actually contains the words if and then. Sometimes, as in this case, these words are implied. First translate the rule into proper if/then form: Including biology anytime history is included essentially means that if history is included, then biology is included. The reverse and negate technique works for any conditional statement, regardless of game type, so we can apply it here to derive the rule’s logical equivalent: If no biology, then no history. Here are both statements in shorthand form:
If H, then B
If NO B, then NO H
Now work through the Positive Conditional in our trusty Placing game.
Economic Seminars: Placing

The participants of two economic seminars, one on free trade and one on venture capital, are to be assigned from among six company employees—Jobson, King, Lee, Manute, Nora, and Orson. King and Nora are vice presidents; the rest of the employees are middle managers. Each employee must participate in at least one seminar. The following rules govern the assignment of employees to seminars:

Rule: If Nora participates in the seminar on free trade, then Jobson participates in the seminar on venture capital.

Here’s the shorthand of the original rule, plus the result of reverse and negate:
If N ft, then J vc
If J NOT vc then N NOT ft
Since the only seminars are free trade and venture capital, we can take this one step further:
If J ft, then N vc
Hopefully you’re getting the hang of working with Positive Conditionals. Let’s try one more example in the context of our Linking scenario.
Birthday Party: Linking

Six children—Edel, Francie, Gillian, Holly, James, and Kayli—attend a birthday party. Three of the children are in nursery school, two are in first grade, and one is in second grade. Each child eats either pizza or a sandwich at the party. No child eats both kinds of food. The following must obtain:

Rule: If James eats pizza, Francie is in nursery school.

Here’s the shorthand of the original rule, plus the result of reverse and negate:
If J pizza, then F nurs
If F NOT nurs, then J NOT pizza
Sounds reasonable, but you’d be negligent to leave it at that. “Not nursery school” means first or second grade, and “not pizza” means “sandwich,” so this last statement can be rewritten in the positive as:
If F 1st or 2nd, then J sandwich
With this info under our belts, how nice would it be for a question to place Francie in first or second grade, and then ask what must be true? “James does not eat pizza” would be a fine answer to allow us to cash in on this work. Or the question might ask what CANNOT be true, in which case “James eats pizza” would get the point. Anyway, we’re getting a bit ahead of ourselves, since cashing in comes after we’ve dissected the rules and tried our best to Search for Game Breakers, Step 3 of our Essential Strategy. But you can see where we’re heading. Let’s get back to the present discussion with a look at the next complex rule type—Negative Conditionals.
Negative Conditional
Negative Conditional rules also consist of if/then statements and statements that can be translated into if/then statements. However, unlike Positive Conditionals, these specify that when one thing happens, another thing doesn’t happen. Here are some examples for each of the major game types.
Art lectures: Ordering

Seven works of art—P, Q, R, S, T, V, and W—will be exhibited at a local gallery opening. A short lecture will be delivered by the creator of each work during the gallery opening. No two lectures will be delivered at the same time. The sequence of lectures must satisfy the following requirements:

Rule: If the lecture on artwork Q is third, then the lecture on artwork V is not fifth.

The key to using reverse and negate for Negative Conditional rules is to remember that two negatives make a positive. In the Ordering rule above, the negation of “V NOT fifth” is “V fifth.” So here’s how we can shorthand the rule, and its logical implication:
If Q3, then V NOT 5
If V5, then Q NOT 3
Let’s apply this to one of the more complicated Ordering rules discussed earlier:

Rule: If the lecture on artwork R is second and the lecture on artwork T is fourth, then the lecture on artwork W is not fifth.

Here’s a shorthanded version of the rule plus the result when we apply reverse and negate:
If R2 and T4, then W NOT 5
If W5, then NOT BOTH R2 and T4
Negating a negative statement turns it into a positive statement.
Try the next one based on our Choosing game intro.
Maggie’s Courses: Choosing

Maggie must select exactly three introductory courses for the upcoming semester. The available introductory courses are biology, communications, English, French, history, literature, and philosophy. Her selection must accord with the following conditions:

Rule: If biology is selected, history is not selected.

Here’s the rule and its logical equivalent in shorthand form:
If B, then No H
If H, then NO B
Notice that in this case the upshot is that biology and history can never be included together in the group of courses Maggie selects.
Now try it with Placing.
Economic Seminars: Placing

The participants of two economic seminars, one on free trade and one on venture capital, are to be assigned from among six company employees—Jobson, King, Lee, Manute, Nora, and Orson. King and Nora are vice presidents; the rest of the employees are middle managers. Each employee must participate in at least one seminar. The following rules govern the assignment of employees to seminars:

Rule: If Nora participates in the seminar on free trade, then Jobson does not participate in the seminar on venture capital.

Here’s the shorthand of the original rule, plus the result of reverse and negate:
If Nft, then J NOT vc
If Jvc, then N NOT ft
Since in this case free trade and venture capital are the only two seminars, we can take this one step further:
If Nft, then Jft
If Jvc, then Nvc
Bring it on home for Negative Conditionals with the Linking scenario . . .
Birthday Party: Linking

Six children—Edel, Francie, Gillian, Holly, James, and Kayli—attend a birthday party. Three of the children are in nursery school, two are in first grade, and one is in second grade. Each child eats either pizza or a sandwich at the party. No child eats both kinds of food. The following must obtain:

Rule: If James eats pizza, Francie is not in nursery school.

Here’s the shorthand of the original rule, plus the result of reverse and negate:
If J pizza, then F NOT nurs
If F nurs, then J NOT pizza
Can we take this one step further as well? Yup, and we should since it’s always best to gather as much positive information as possible. “Not nursery school” means first or second grade. “Not pizza” means “sandwich.” So here’s our final understanding of this rule:
If J pizza, then F 1st or 2nd
If F nurs, then J sand
Unless
Some rules are built around the word unless. On the LSAT, you might see a rule indicating that a certain thing can’t happen unless something else happens. Here’s an example.
Maggie’s Courses: Choosing

Maggie must select exactly three introductory courses for the upcoming semester. The available introductory courses are biology, communications, English, French, history, literature, and philosophy. Her selection must accord with the following conditions:

Rule: Biology is not selected unless history is selected.

To say that biology is not selected unless history is selected is the same as saying that biology requires history:
If B, then H
To which we can now apply reverse and negate:
If NO H, then NO B
Notice that the selection of history does not guarantee the selection of biology—it merely makes it possible. There’s no equivalency beginning “If H . . .” because if history is selected, biology may be selected, but it need not be. All we know for sure from this “unless” rule are the two if/then statements listed above.
Either
Some rules contain the word either. Here are a few examples to chew on for the Ordering and Choosing game varieties.
Art Lectures: Ordering

Seven works of art—P, Q, R, S, T, V, and W—will be exhibited at a local gallery opening. A short lecture will be delivered by the creator of each work during the gallery opening. No two lectures will be delivered at the same time. The sequence of lectures must satisfy the following requirements:

Rule: The lecture on artwork T is either first or sixth.

The implications are that if some lecture beside T’s lecture is first, T’s must be sixth, and if some lecture beside T’s lecture is sixth, T’s must be first.
Here’s another way either can be used in an Ordering rule:

Rule: Either the lecture on artwork T or the lecture on artwork V must be third.

In this case, it makes sense to jot down T/V above the third slot in your blueprint. As soon as you see one of those characters in some other spot, you can pencil the other character into spot 3.
Now see how either plays out in the context of a Choosing example.
Maggie’s Courses: Choosing

Maggie must select exactly three introductory courses for the upcoming semester. The available introductory courses are biology, communications, English, French, history, literature, and philosophy. Her selection must accord with the following conditions:

Rule: Either communications or philosophy will be selected.

That means that a group with communications but not philosophy is okay. A group with philosophy but not communications is also okay. A group with both communications and philosophy is also okay.
Wait a minute—that seems counterintuitive to many, since the rule seems to say that we need either one or the other. However, on the LSAT the idea “but not both” will be included in the rule if the intention is that both characters cannot be included in the group. The only thing that violates the rule as stated above is a group of chosen courses that includes neither communications nor philosophy.
If you’re having trouble interpreting a rule, think about what scenarios would violate that rule. That should help you zero in on what the rule really means and how it will play out throughout the game.
Only If
An “only if” statement can be turned into an if/then statement by placing the “then” after the “only” term. For example, consider the following Placing rule.
Economic Seminars: Placing

The participants of two economic seminars, one on free trade and one on venture capital, are to be assigned from among six company employees—Jobson, King, Lee, Manute, Nora, and Orson. King and Nora are vice presidents; the rest of the employees are middle managers. Each employee must participate in at least one seminar. The following rules govern the assignment of employees to seminars:

Rule: Orson participates in the seminar on free trade only if King participates in the seminar on venture capital.

There are two parts of an “only if” statement: the part attached to the “only if” phrase (here, K vc) and the other condition in the statement (here, O ft). This other condition—in this case, Orson joining free trade—relies on the “only if” condition. Here, that means that if Orson participates in free trade, then King must participate in venture capital; the “only if” phrase in the statement demands this. So we can turn this “only if” statement into a standard if/then statement, like so:
If O ft, then K vc
In fact, we can even derive a general rule from this: For any “only if” statement, throw an “if” in front of the other condition and a “then” in front of the condition associated with the “only if” phrase and you’ll end up with a valid statement in the form of “If X, then Y.” It sounds confusing, but go back to look how we applied this rule to the example above and it should eventually click. The beauty of restating the “only if” statement as an if/then statement is that now we can apply reverse and negate to yield yet another valid statement:
If K NOT vc, then O NOT ft
Do we stop there? No! Remember to translate negatives into positives whenever possible. Since the only choices in this game are free trade and venture capital, we can get rid of the two NOTs:
If K ft, then O vc
That’s a lot of information derived from a seemingly innocuous “only if” rule, but that’s what Logic Games success is all about.
If and Only If
What if we add an “if” to the “only if” statement? Let’s use the same Placing rule to find out.
Economic Seminars: Placing

The participants of two economic seminars, one on free trade and one on venture capital, are to be assigned from among six company employees—Jobson, King, Lee, Manute, Nora, and Orson. King and Nora are vice presidents; the rest of the employees are middle managers. Each employee must participate in at least one seminar. The following rules govern the assignment of employees to seminars:

Rule: Orson participates in the seminar on free trade if and only if King participates in the seminar on venture capital.

The interpretation of the “only if” part of the rule remains the same as what we just deduced:
If O ft, then K vc
If K ft, then O vc
However, we must also take the “if” part into account:
If K vc, then O ft
Using reverse and negate and translating negatives to positives yields:
If O vc, then K ft
Here’s the difference: The “only if” rule allows for the possibility that King and Orson participate together in the seminar on venture capital. The “if and only if” version of the rule does not allow for this possibility. It forces these two employees to split up, no matter what. The test makers don’t use “if and only if” very often, but they have in the past, and nothing stops them from doing so in the future. Your confidence will increase when you go into the test feeling as if you’re ready for anything they may throw your way.
That does it for Step 2, Get the Specs. The specs of the game are mainly spelled out in the rules, although some important specifications, especially number information, may be included in the introduction as well. The line between what we call Conventional and Complex rules may blur in cases. For example, some Conditional rules may become simple to you with practice, while a Number rule may throw you for a loop. Don’t get hung up in the terminology—just study the categories above until these kinds of rules discussed, and their logical equivalencies, make sense and become second nature to you. Hopefully, even the toughest of rules will seem conventional to you by test day. The examples above cover the majority of rule scenarios you’ll come across, but you’ll likely encounter variations and combinations as well. You’ll get plenty of practice working with rules from the eight games in this book. Extend what you learn from this section, and from those eight games, to every practice game you try.
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