The 2024 Olympic Games in Paris are currently captivating the world with displays of athletic excellence, national pride, and the celebration of human potential. Behind the scenes, meticulous planning ensures that every detail, including the medal ceremonies, proceeds flawlessly. 

The challenge of preparing for these ceremonies was uniquely addressed by participants in the 2023 Middle Mathematical Contest in Modeling (MidMCM). Middle school student participants were tasked with creating models to predict the number of medals and flags required, ensuring the ceremonies would run smoothly without overspending.

The Scope of the Challenge

The Paris 2024 Olympic Games host athletes from 203 National Olympic Committees (NOCs), competing across 40 sports with a total of 329 medal events. Each event awards three medals: Gold, Silver, and Bronze, and the flag of the winning country is displayed during the ceremonies. Given this complexity, predicting the exact number of medals and flags needed is a substantial logistical task.

The MidMCM Problem

In 2023, the MidMCM problem challenged students to develop mathematical models to help the International Olympic Committee (IOC) prepare adequately for the 2024 Games. The problem required the participants to balance two primary objectives: ensuring enough medals and flags for every ceremony and avoiding unnecessary overspending by ordering too many.

Key Components of the Problem

1. Event Breakdown: The teams had to analyze each sport, which could include multiple events with separate categories for men, women, and mixed teams.
2. Medal Distribution: Each event awards three medals, and the number of athletes receiving medals varies for individual and team events.
3. Flag Requirements: Each ceremony involves displaying the winning countries' flags, with the number of flags depending on the unique countries winning medals in each event.

Developing the Models

Middle school participants were asked to choose one of three major venues and develop a schedule for the medal ceremonies. Based on this schedule, they created models to determine the number of medals and flags needed for their chosen venue. This approach included:

1. Scheduling Ceremonies: Estimating the number of medal ceremonies based on the events hosted at the venue.
2. Medal Count Model: Calculating the minimum, maximum, and optimal number of medals required.
3. Flag Count Model: Estimating the number and types of flags needed.

Application and Impact

After creating models for their chosen venue, participants applied these models to other venues, eventually extrapolating the results to cover the entire Olympics. This comprehensive approach ensured that the IOC could order the correct number of medals and flags, avoiding both shortages and excess.

The Real-World Application

As the Paris 2024 Games unfold, the careful preparation like that of the MidMCM participants' models is evident. The IOC's ability to predict the necessary number of medals and flags accurately has allowed the ceremonies to proceed seamlessly, showcasing the success of these mathematical models in a real-world setting.

The 2023 MidMCM problem demonstrated the power of mathematical modeling in solving real-world logistical challenges. By applying their analytical skills to the preparation of the Olympic medal ceremonies, middle school participants have shown how math can play a critical role in global events. As the 2024 Olympic Games continue to inspire and amaze, we can appreciate the behind-the-scenes efforts that make such an international celebration possible.

Learn more about the MidMCM math modeling contest, and explore why you should participate in the next middle school math contest.