Overview of game types - Matching games

Learning Outcomes

After reading this article, you will be able to identify the structure and core features of LSAT matching games, distinguish matching games from other logic game types, accurately diagram setups and rules, efficiently apply deduction strategies, and avoid frequent pitfalls. Proficiency in these areas is essential for success in the Analytical Reasoning (Logic Games) section of the LSAT.

LSAT Syllabus

For LSAT, you are required to understand the range of game types presented in Analytical Reasoning (Logic Games). For this article, focus your revision on:

• the distinctive features and structures of matching games as compared to ordering and grouping games
• the core rules, elements, and relationships commonly encountered in matching games
• diagramming best practices for setups and translating rules accurately
• strategies for deductions and identifying rule interactions in matching games
• time-efficient approaches for solving LSAT matching games under exam conditions

Test Your Knowledge

Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision.

1. Which aspect most distinguishes a matching game from a pure grouping game on the LSAT?
   1. Elements are placed into a strict sequence
   2. Each element must be matched to one or more attributes or categories
   3. Only one variable is tracked throughout the game
   4. No elements can remain unassigned
2. Which of the following is a likely rule format in an LSAT matching game?
   1. G must be placed before H in the sequence
   2. T and Y cannot be in the same group
   3. If L is assigned to project 1, J must be assigned to project 2
   4. Each consultant must be assigned to exactly two regions and one industry

3. True or false: In matching games, drawing a two-dimensional diagram is usually necessary to track all assignments and rule interactions.

Introduction

Matching games are a core LSAT game type in the Analytical Reasoning section. These games require you to pair, assign, or connect items (such as people, companies, or events) with multiple sets of attributes or categories (such as colors, projects, or locations). Success depends on understanding the typical structures, efficiently diagramming, and applying rule-based deductions.

What Is a Matching Game?

A matching game asks you to assign items from one set (e.g., five students) to items or properties from one or more other sets (e.g., four language classes, three sports teams). Unlike pure ordering (sequence) or grouping (in/out, teams), matching games involve relationships between two or more variable types.

Key Term: matching game
A logic game in which elements from one set must be assigned, paired, or connected to elements from one or more additional sets, typically under a set of specific rules and constraints.

Identifying Matching Games

Matching games can be recognized by:

• Two or more independent variable types (e.g., employees and departments, vehicles and colors)
• Each item must be matched to at least one category or attribute (sometimes more)
• Assignments may be "one-to-one," "one-to-many," or "many-to-many," depending on the game's rules

Typical Structures

LSAT matching games often use these elements:

• A given list of primary items, such as people or places
• One or more sets of attributes, such as tasks, days, categories, or qualities
• Rules specifying how many assignments each item must or may have, and various restrictions (some elements may remain unmatched, while others must be assigned to several attributes)

Key Term: one-to-one matching
Each item in the main set is assigned to exactly one item from another set.

Key Term: one-to-many matching
Each item in the main set can or must be matched to more than one item from another set.

Diagramming Matching Games

A clear diagram is essential. For most matching games, construct a table or grid with:

• Primary items as rows, attributes as columns (or vice versa)
• Placeholders to mark possible and required assignments
• Notation for forbidden assignments (e.g., slashes) and fixed ones (e.g., circles or checkmarks)

A simple one-to-one matching game may look like this:

A more complex one-to-many matching will require additional marks to show multiple matches (such as tick marks or numbers).

Worked Example 1.1

A set of four musicians (K, L, M, N) must each play at least one of three genres: jazz, rock, or classical. Each genre must be matched to at least one musician, and each musician can play more than one genre. Rule: If K plays jazz, then N cannot play jazz.

How would you set up a diagram for this matching game, and what deduction can you make if both K and N play jazz?

Answer:
Use a table with musicians as rows and genres as columns, with marks for possible assignments. The rule leads to a deduction: it is IMPOSSIBLE for both K and N to play jazz; if K plays jazz, N is excluded from jazz. If N does play jazz, K cannot. Your diagram should clearly record this restriction.

Common Rule Types in Matching Games

Matching games use several types of rules:

• Assignment requirements: "Each project manager must oversee at least one project."
• Prohibitions: "G cannot be assigned to the West region."
• Conditional logic: "If team 3 gets the Alpha client, then team 1 cannot have Bravo."

Be especially attentive to minimum and maximum assignment numbers, and rules stating "at least" or "no more than" a given value.

Key Term: assignment constraint
A limitation specifying how many times or in which combinations assignments can occur (e.g., "each engineer is assigned to exactly two projects; each project has no more than three engineers").

Making Deductions

In matching games, deductions often result from overlapping assignment constraints, fixed assignments, or conditional rules. Look for:

• Elements or attributes with limited assignment options due to other assignments already made or rules in place
• Contrapositive applications in conditional rules (negating and reversing the original statement)
• Distribution deductions (e.g., when knowing X is assigned, Y cannot be, and vice versa)

Worked Example 1.2

Suppose a game involves three interviewers (J, K, L) and five candidates (W, X, Y, Z, Q). Each candidate must be interviewed by exactly two interviewers, and no interviewer sees more than four candidates. Rule: If K interviews Y, then J cannot interview Y.

If K interviews Y, what deductions can you make about J and Y?

Answer:
In this setup, if K interviews Y, the rule forces J NOT to interview Y, so the two required interviews for Y must be K and L. Furthermore, J will have one less candidate available, tightening J's overall options.

Efficient Approaches to Matching Games

• Diagram all elements and categories visually
• Systematically note all rule-based restrictions in your grid or table
• Search for elements with the fewest assignment possibilities; resolve these first
• After each question that adds or changes a rule, redraw or update your diagram for clarity

Exam Warning

On matching games, failing to track double assignments (where an element is matched to more than one attribute) is a common cause of error. Always record every required assignment and prohibit duplicates where stated by the rules. Missing a minimum or maximum assignment constraint can invalidate your answer.

Revision Tip

When reading rule sets in matching games, highlight or underline assignment numbers (e.g., "exactly three," "at least one") to ensure your diagram accurately reflects all constraints before attempting deductions.

Summary

Key Point Checklist

This article has covered the following key knowledge points:

• A matching game involves assigning elements from one set to attributes from other sets under rule-based constraints
• Diagrams for matching games should use tables or grids to track all possible and forbidden assignments and attribute combinations
• Typical matching game rules involve minimum/maximum assignment numbers, prohibitions, and conditional constraints
• Deductions often depend on overlapping rules, assignment constraints, and the contrapositive of conditional statements
• Double-check diagrams after each rule or question-specific change to track evolving assignment possibilities

Key Terms and Concepts

• matching game
• one-to-one matching
• one-to-many matching
• assignment constraint