Grouping Game Tutorial

In a Grouping game you are given a list of entities and asked to place them in groups.. A good diagram is essential for a Grouping game and you will often need to re-draw the diagram for each question. The rules in a Grouping game will often include things such as: Entity A is in group 1, or Entity A is in the same group as Entity B, or Entity C can not be in the same group as Entity C. In some Grouping games each entity can only be used once. These are Grouping Distribution games as you are distributing a limited number of entities into groups. Some grouping games will allow you to use the same type of entity many times or an unlimited number of times and place them in more than one group. These are Grouping Selection games because you have different types of entities to select from and put into groups. The key difference between a Grouping Distribution game like this one, and a Grouping Selection game that has more than one of each entity.

Grouping Distribution Example:

Six people, Sean, Michael, Tina, Cecilia, Anne, and Ryan are going out on Friday night. Each person goes to one of three locations. The Mod Club, Lou’s Tavern, or the House of Blues.
Sean and Michael do not go to the same location.
Ryan and Anne go to the same location.
If Tina goes to a location Cecilia also goes to that location.

Notice that you have a limited number of people to distribute amongst the locations. Once you have selected Sean to go to a location he cannot also go to other locations. Each person only goes to location. The bold statement tells you enough to know that this is a Grouping Distribution game.

Grouping Selection Example:

There are five types of fruit, oranges, apples, bananas, pears, and kiwis being sold at three different fruit stands. Each stand carries a maximum of four types of fruit and a minimum of one type of fruit.
The first stand does not carry oranges.
Any stand that carries apples also carries bananas.
No stand carries both kiwis and oranges.

Notice that you can put oranges, or any type of fruit, in multiple fruit stands. Just because one stand carries kiwis does not mean that another stand can’t also carry kiwis. Unlike the Grouping Distribution game where once an entity is placed it has been used up and can not be placed elsewhere.

Entities or Groups?

In Grouping games you are given two sets of items, such as dogs and days of the week. One difficulty that people often encounter in a grouping game is determining which are the entities and which are the groups. For example you might try making the dogs the groups and placing the days of the week with the dogs instead of the other way around. Generally the question sets it up for you so that it obvious which are the groups and which are the entities. If you struggle with deciding which set should be the groups usually the LSAT question will list the groups second. Also if they tell you how many spots are available then that is a good set to use as a group. For example in this game they tell you that there are two spots on each weekday. This information makes it easier to use the weekdays as groups. If you really can not decide then just pick one and move on with the game. You can get all the correct answers no matter which set you make the groups or the entities.

The following are good clues to tell you which set of items should be the groups:

• The question tells you how many spots are available in the group
• If there are many of one type of entity in a set available and only one of each of the other set then the second set will make better groups. For example if there are 3 huskies, 2 poodles, and 5 keeshounds as one set and only one of each of Monday, Tuesday, and Wednesday then the days of the week make the best set of groups and the dogs should be the entities placed into the groups.
• The groups are often listed second.
• If you are setting up your diagram and it seems too complicated or not much information is easily transferable to your diagram, or it just doesn’t make much sense to you then try switching and using the other entity as a group.
• The more Grouping games you do the easier it will become to pick out the best set for the groups.
• If there are multiple entities of each type allowed then they must be the entities and the other set will be the groups. This is a Grouping Selection game and the multiple entity set is never the groups. For example in the fruit stand Grouping Selection example above the stands must be the groups and the fruit must be the entities because you can have more than one of each type of fruit. This makes selecting which set is the entities and which is the groups easy in a Grouping Selection game.

Maximum and Minimum spaces in a group

In a grouping game each group will have a maximum and a minimum number of entities that can fit into that group. The minimum could be as low as none and the maximum could be unlimited. If you can determine the maximum and minimum number of entities in a group it will make solving each question much easier. This information is easy to add to your diagram with a simple diagramming technique. When you want to list the minimum number of spots in a group simply use solid lines below the group title, one line for each spot. You now know that in order for your diagram to be filled in correctly you must put an entity on each solid line. The maximum number can then be represented by dotted lines as they may or may not be filled in with an entity, but you know you can not place any more entities in a group than the number of solid and dotted lines.
Example:

Six students, Joe, Sarah, Liz, Will, Kyle, and Jessica will be placed in three classes, physics, math, and English. The classes are your groups and the students are your entities. You are told that the physics class can have a minimum of two students and that no class can have more than three students. Also, at least one student takes math.
The diagram can be set up as follows:

P M E (These are your groups)
__ __ …
__ … …
… … …

We see that under physics we have two solid lines and one dotted line representing a minimum of two students (we must fill all solid lines) and a maximum of three students (we may fill dotted lines but we don’t have to, and we can’t put any more students in than we have dotted lines for).
Math has a minimum of one and a maximum of three and English has no minimum (we don’t have to put any students in English) and a maximum of three students.

Tricks for determining maximums and minimums

Often the maximum or minimum number in a group is not given but it can be determined by combining rules or other information. A key piece of information is the total number of entities. In our example of students and classes we have three classes and six students. If the game is as follows: Six students, Joe, Sarah, Liz, Will, Kyle, and Jessica will be placed in three classes, physics, math, and English. Each student can only take one class. You are not told anything about maximum class sizes but you are told that each class has a minimum of one student. Can you determine the maximum number of students for each class?
If we have three classes and each must have a minimum of one student then once we place a student in each class we only have three students left. If we put all these students in one class we have four students in that class and one in each of the other two classes.

P M E
J S L
W
K
J

There is no way to put more than four students in a class. To do this we would have to take a student out of one of the other classes breaking the rule that there is a minimum of one student per class. So our maximum number of students for each class is four. You can fill this in on the diagram as follows:

P M E
__ __ __
… … …
… … …
… … …
… … …

Note that this trick will not work if you are allowed to place the same student in many classes. Then we would have a maximum of six students per class. As potentially each student could be in all three classes.

Now that you have completed this Grouping Game tutorial try another Grouping Game.

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