Previous problem 2025

IMMC Global Sports League

Background

Fair competition in sports requires a balance of logistics, equity, and practicality, especially when organizing sporting competitions on an international scale. The International MultiContinental Matchmaking Committee (IMMC) seeks your expertise to develop a scheduling system for their upcoming Global Sports League (GSL). This league will feature teams from around the world, emphasizing geographic diversity, competitive equity, and logistical feasibility.

The IMMC also values economic and environmental sustainability, wants to ensure fair matchups and requires the league to include 20 teams with at least two teams from each continent (excluding Antarctica). The GSL season runs between 8 and 9 months. While the IMMC has outlined key criteria for the league, they have not yet determined the sport to be played in the GSL. Some sports already have an established international presence, while others have limited global reach. The IMMC is open to considering any team sport, provided your team can demonstrate its potential for global expansion within the GSL framework. This is where your expertise is needed. Your team is invited to select a sport you are passionate about, develop a model that produces a fair and effective schedule for the GSL, and test how well your scheduling model adapts to changes in the league.

Outstanding Achievement solutions

Solution 1 Solution 2

IMMC Problem

Your task:

  1. Identify key factors
    1. What is the sport? The GSL is a team sport competition (see Glossary for details).
    2. Who are the teams and where are they located? Identify 20 teams to participate, ensuring at least two teams represent each continent (excluding Antarctica). Clearly explain the criteria used to select these teams.
    3. What aspects need to be considered when building a league schedule? The IMMC expects the schedule to consider travel distance, the number of games played and equitable matchups, but they are unsure of other components that may be of importance. Identify any additional key components that should be considered when developing a fair GSL schedule and discuss trade-offs involved in balancing these factors.
  2. Develop the initial schedule
    Build a mathematical model to construct a fair and practical schedule for the 20 team GSL. At the very least, ensure your scheduling model accounts for
    1. Fair distribution of games across teams,
    2. Equitable travel time and distance,
    3. Balanced competitiveness of matchups.
      Use your model to create a full season league schedule for your selected sport and provide evidence that demonstrates how it achieves IMMC goals of fairness, sustainability, and geographic representation. Additionally, determine the number of games each team must play to reasonably declare a league winner at the conclusion of the season.
  3. Expand the GSL and extend the model
    1. Add four teams to the Global Sports League. Clearly explain the criteria used to select these teams.
    2. Evaluate how this expansion impacts the league schedule. Make sure to address fairness, sustainability, and geographic representation.
    3. Assess how the addition of four teams impacts the number of games that need to be played by each team in order to reasonably declare a league winner.
    4. Analyze how changes to key constraints (e.g., travel distances, change in home location of a team, number of league games) impact your model.
  4. Generalize the model
    In two pages or less, discuss how one could adapt your model to different team sports with distinct rules, game lengths, and team dynamics
  5. Communicate your solution to a non-technical audience
    1. Write a one-page letter to the IMMC summarizing your findings. In your letter, explain how your model aligns with the IMMC’s goals for the league. Ensure your explanation is accessible to a non-technical audience.
    2. Provide a visual graphic of the initial 20-team GSL schedule on a separate page.

Glossary

Team Sport

A team sport is a sport in which multiple players collaborate to achieve a common objective, ultimately leading to victory in a game or match. To qualify for potential inclusion in the GSL, the sport must require a minimum of five players per team actively participating on the field, court, or playing area at all times throughout the match.

Examples of eligible sports (non-exhaustive): football (soccer), basketball, cricket, rugby, American football, volleyball, handball, water polo, and lacrosse.

Visual Graphic

A visual graphic is a visual representation of information, data, or ideas, typically combining images, text, and design elements to communicate a message effectively.

2025 IM2C Full Submission Guidelines

Teams may use any inanimate source of data, materials, computers, software, references, websites, books, etc. Be sure to credit all sources used.

Teams may not use any person (other than team members) to discuss or obtain ideas for solving their problem nor may they seek help in obtaining an answer from the teams' advisor or anyone else. Any team that discusses the problem with anyone in a position to supply them with information reflecting experience or professional expertise will be disqualified. The relevant issue is one of intent: each team of students is expected to develop all of its substantive analysis without the help of others.

Partial solutions are acceptable. There is no passing or failing cutoff score, nor will numerical scores be assigned. The IM2C judges are primarily interested in a team’s approach and methods.

The solution must consist entirely of written text and possibly figures, charts, or other written material only. No non-paper support such as computer disks or applications will be accepted.

Each page of the solution should contain the team control number and the page number at the top of the page; we suggest using a page header on each page for example: Team #2024000 page 6 of 13.

The names of the students, advisor, or institution must not appear on any page of the solution. The solution must not contain any identifying information other than the team Control Number.

Submission Paper Requirements

  • One-page Summary Sheet
  • One-page Table of Contents
  • One-page Letter to the Decision Makers with your recommendation
  • One-page Visual Graphic of the initial 20-team GSL schedule
  • Complete solution (maximum 20 pages)
  • Reference List
  • AI Use Report (if used)

Note: The Reference List and Appendices (including AI Use Report) do not count towards the 24-page limit.

Your PDF submission paper must be typed and in English using A4 (minimum 1.5cm margins) or Letter (minimum 0.6in margins), and at least 12-point font size.

General Formatting Guidelines

  • Conciseness and organization are extremely important.
  • Clarify or restate the problem as appropriate.
  • Clearly state all variables, assumptions, and hypotheses.
  • Present an analysis of the problem with justifications.
  • Include a model design and discuss how it could be tested.
  • Discuss strengths and weaknesses of your approach.
  • Place lengthy derivations, computations, or examples in appendices.
  • Explicitly state results in the main report.

Required Pages Description

Summary Sheet

Summarize the problem, main solution approach, and your conclusions. Make it compelling to encourage further reading.

Table of Contents

Enables the reader to find various sections easily, especially for non-sequential reading.

Letter to the Decision Makers

Addressed to the Directors of the IMMC, the letter should concisely present your recommendation and insights from your solution. Keep it persuasive and accessible.

Visual Graphic

A one-page graphic that is clear, engaging, and designed for a non-technical audience. It should visually summarize key insights from your 20-team GSL schedule.

Twenty-page Solution Report

Your main body should include essential details about your methodology and findings.

Specifications

  • Paper must be in English
  • A4 or Letter format with required margins
  • At least 12-point font
  • All pages including summary, graphic, letter, and TOC count towards 24-page limit

Compliance

Failure to meet these specifications or attempts to circumvent them may result in a lower designation or disqualification.

Reference List, Appendices, and AI Use Report

These do not count toward the 24-page limit. You must cite all sources clearly and ensure your solution is your own original work. Unauthorized use of copyrighted material may result in disqualification.

Australian judges' commentary