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Search for Game Breakers
As we discussed, we’ve added an extra step between tackling the introduction
and the rules and tackling the questions. Now that you’ve created your blueprint and
mapped out the specs of the game by analyzing the rules individually, the next
important step is to combine the rules to form deductions: additional conditions not
explicitly stated but that nonetheless must be true based on the given information.
We call such deductions “Game Breakers” because of their ability to break the game
wide open. Game Breakers come in three major varieties:
- Standard Combinations
- Number Crunching
- Restricted Possibilities
Let’s get some practice with each.
Standard Combinations
Some rules link up fairly easily. For example, consider the following two
rules:
If X is selected, then Y is selected.
If Y is selected, then Z is not selected.
Now, they don’t come right out and say it, but it must be true that
selecting X means NOT selecting Z. This is a simple matter of putting two and
two together.
Whenever you form a deduction, add it to your list of
shorthanded rules. A valid deduction applies throughout the entire game
exactly as if it were a given rule.
Now try one on your own. Consider the following game setup. Combine the
rules to deduce as much additional information as you can.
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: Francie and James are in the same grade. No first grader eats a sandwich. Exactly two nursery school children eat pizza. James does not eat pizza. |
Rule 4, a Direct Negative, is the best place to start.
You don’t have to tackle the rules in the order
in which they’re presented. It’s better to begin with the most concrete
rule first, because it’s easier to build the rest of the rules around
that definite information.
If James does not eat pizza, James must eat a sandwich.
Rule 1 contains James too, so let’s go there next.
Pay careful attention when more than one rule
contains the same character. That’s a clue that Game Breakers may be
lurking in a combination of those rules.
If Francie and James are in the same grade, that must be nursery
school or first grade, since there’s only one second grader. But Rule 2 says
that no first grader eats a sandwich, and we’ve already determined from Rule
4 that James does eat a sandwich. So Francie and
James must be in nursery school. Rule 3 then allows us to
determine that Francie must eat pizza, since James must be the
one nursery school sandwich eater, leaving Francie and one other child as
the two nursery school pizza eaters.
Notice how we’ve already pinned down the complete status of two of the
six children, before even getting to the questions. Having this extra
information at the start will definitely make the game much easier. A
standard combination of rules led us to these Game Breakers.
Number Crunching
We’ve seen already (including in the previous example) how working the
numbers of the game can lead to new and important information. Number rules may
appear in the game’s introduction, or in the indented rules. Wherever you see
numerical information, see if you can push it further.
Consider the following game setup. See if you can crunch the numbers to
yield new information.
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: Jobson does not participate in the same seminar as Manute. There is at most one vice president participating in each seminar. If King participates in a seminar, Lee participates in that seminar. There is exactly one more middle manager than vice president at the seminar on venture capital. |
The introduction indicates that there are exactly two vice presidents,
King and Nora. We can combine this with Rule 2 to deduce that King and Nora
cannot attend a seminar together. “At most one VP in each” means that two
VPs at a single seminar is a no-no. So King attends one seminar, while Nora
attends the other. Rule 3 involves King, so it makes sense to look there
next. Wherever King is, Lee is. So now for starters we have KL on one side,
and N on the other. It doesn’t matter that we don’t yet know exactly which
seminars these people attend.
In Placing games, knowing who must and must not
be placed together can be just as important as knowing where they are.
Drive the information forward in any way you can.
The fact that we know exactly how many VPs are at each seminar (one)
sheds a whole new light on Rule 4: It allows us to determine that there must
be exactly two middle managers at the venture capital seminar. This fact
that may yield a point all on its own, but it will also no doubt be of help
in answering all of the questions. Any time rules involve numbers, drive the
information as far as you can. Often, games that seem wide open get pretty
well defined after you crunch the numbers.
Restricted Possibilities
In cases in which only two options are possible (such as when a character
can go in only one of two spots), it’s worth your while to check out what
happens in each case. In the best case scenario, you’ll be able to create two
options of the game’s universe, leaving very little up in the air. Here’s the
game we were just working on, except that we’ve made a small change in the
opening paragraph. Find the difference and then take the information as far as
you can.
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 exactly one seminar. The following rules govern the assignment of employees to seminars: Jobson does not participate in the same seminar as Manute. There is at most one vice president participating in each seminar. If King participates in a seminar, Lee participates in that seminar. There is exactly one more middle manager than vice president at the seminar on venture capital. |
Did you see the difference? Now each employee participates in exactly
one seminar. Let’s see where that takes us. We already concluded that there
must be exactly three participants in the venture capital seminar (one vice
president and two middle managers). But if each employee is in only one
seminar, then the other three employees must be in the free trade seminar.
Some test takers would stop their search for Game Breakers at this
point and move on to the questions, and some may even do fairly well on the
game. But the best Logic Games practitioners would recognize an opportunity
to drive the information even further.
We just discovered through Number Crunching that King, Lee, and one
other employee must participate in one of the seminars, while Nora and the
remaining two employees must participate in the other. Since there are only
two seminars, there are only two ways we can do this: Place King in free
trade or place Nora in free trade. Let’s see what happens in the first case:
Possibility 1: K ft
|
FT
|
VC
|
|
K L __
|
N __ __
|
Now we can incorporate Rule 1. We have to split up Jobson and Manute,
and there’s only one space left in free trade, so one of them must go there
while the other must attend venture capital. We don’t know which is which
yet, but notice what this reveals: Orson, the only employee left, must take
the final spot alongside Nora in venture capital. So Possibility 1 boils
down to this:
Possibility 1: K ft
|
FT
|
VC
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K L (J/M)
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N O (J/M)
|
Pretty good. We now know everything that happens when King is the VP
in free trade, except for the placement of J and M. The only other possible
option is to place Nora in free trade, and the same scenario plays out.
Possibility 2: N ft
|
FT
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VC
|
|
N O (J/M)
|
K L (J/M)
|
The possibilities are restricted to these two scenarios. In both
cases, Nora must be with Orson, which by extension means that Orson cannot
be with King or Lee. Armed with all of these Game Breakers, the questions
should now fall very quickly. Even a difficult question would merely require
checking the new information given in that specific question against the
restricted possibilities set forth in the two options.
Combining rules, crunching the numbers, and boiling down the
possibilities are three powerful ways to uncover Game Breakers. Not every
game contains them, but when Game Breakers are available, finding them can
turn a killer game into cake.
You may be wondering how long you should look for Game Breakers before
going to the questions. It’s a tough issue. You don’t want to miss major
deductions like the ones you’ve just seen. But you can’t spend all day
looking for stuff that isn’t there.
Here’s the best approach: Look for the important kinds of Game
Breakers you’ve just seen: Standard Combinations, Number Crunching, and
Restricted Possibilities. Then hit the questions. Here’s one more rule of
thumb: Games that have pretty simple setups are less likely to have big Game
Breakers. So if a game seems very easy at first glance, it is less likely to
have Game Breakers that make it even easier. However, a game that looks like
an absolute killer probably has some Game Breakers waiting to be found.
Spend more time up front on the killer games. After a while you’ll get a
sense for when you’ve spent enough time looking for Game Breakers. That’s
just one benefit you’ll get from practicing the skills you learn in this
book.
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