# The MMM, more than the sum of its parts

Maastricht University has its own international maths competition: the Mathematical Modelling competition Maastricht (MMM). The event for high school students has been going strong since 1995.

On the morning of the 25th MMM competition, co-organiser Gijs Schoenmakers casually leans on the sign-up desk. “To give you an idea of how long we’ve been doing this: I guarantee you that in a few minutes, Hans [Peters] will joke that the first exercise is for students to find their rooms.” He grins. And he is right, too.

## 40 teams x 5 high school students x 25 years= 5,000 participants

The small exchange in the lobby is exemplary for the rest of the day. The MMM runs like a well-oiled machine, its formula relatively unchanged over the years. Teams of up to five high school students – mostly travelling from Germany, Belgium and the Netherlands – spend their Saturday afternoon solving mathematical puzzles. Meanwhile, their teachers are free to attend lectures by UM researchers.

*Follow some of the participants during the 25th edition of the MMM on 26 January 2019:*

## 30 students + 4 students = 1 shared problem

These days, the MMM is held purely for the love of mathematics. The math-heavy bachelor’s programmes of the two organizing departments – Quantitative Economics and Data Science and Knowledge Engineering – are flourishing, each drawing triple-digit numbers of students each year.

This hasn’t always been the case. The math competition was originally meant to boost enrolment. Professors Ralf Peeters (DKE) and Hans Peters (QE) are involved with the MMM since the very beginning. “Our two study programmes started out around the same time”, Hans says. “The demand was not exactly overwhelming. I think we had less than thirty students in the first year.” Ralf: “I arrived here in ’94. At the end of that year, I saw the first students. All four of them! It was very obvious that we needed to do something about visibility.”

## 2.5 hours / 5 exercises = panic

Although the reason for hosting the competition changed long ago, the MMM still dishes up five recreational math problems each year. “Some seem very challenging,” says Jean Derks. “But they may be easy to solve if you look at them in a different way. Lean back, take a deep breath and try to figure out what is going on. Don’t frantically start trying things.” Co-organiser Hans Peters agrees. “Once we explain the solutions, students often realize: oh, it wasn’t that hard. But yeah, if you’re sitting there and have only 2.5 hours to solve everything…”

Explaining the solutions at the end of the day is something all organisers look forward to. Ralf Peeters: “The best moment is when I’m up there explaining the answers and you hear a buzz going through the audience. That’s when recognition kicks in: why didn’t we find this solution? Other groups may start shouting: yes! Yes! When we post the scores, it’s devastation and enthusiasm all at the same time.”

## Solution unknown

Of course, some remarkable moments inevitably presented themselves during the competition’s long history. Gijs Schoenmakers remembers how in 2010, he included a problem that even the organization wasn’t sure they had solved. Gijs: “The question was to find the best possible solution. I was very curious to see what they would find, but unfortunately no one topped our answer.” Future participants need not worry though: “It’s the only time we included an unsolved problem.”

Karin van den Boorn recalls two particular events: “Quite a lot of teachers come back every year. Recently, one of them attended for the last time and wanted to take a picture with us as a memory. Another year, we had so many groups participating – around 80 – that we had to use two different buildings. We capped attendance at 40 teams after that.”

## 25 past editions + x future events = …

Naturally, some things were out of the ordinary for the festive 25th edition too. The Tuna de Maastricht played cheerful tunes to welcome participants, for example, and the organization offered anniversary cupcakes as well as a booklet specially made for the occasion.

However, it seems the competition’s core business is not about to change: mere hours after the event concluded, the MMM website immediately announced the preliminary date for next year’s competition. If you enjoy solving the problems presented on this page, you may already want to mark January 25, 2020 in your agenda.

By: Dieudonnée van de Willige (text), Jean Derks (fotography)

*Here are two of the problems of the 2019 edition of the MMM:*

**Problem #3 of the 2019 MMM: Line Dancing**

Professor K makes a euphoric dance after making another scientific breakthrough. The dance consists of 25 equally sized steps, 14 to the left and 11 to the right. So, indeed professor K is performing a line dance. Obviously, at the end of his little dance Professor K is three steps to the left of his starting position.

a. How many different possibilities are there for professor K’s dance?

b. How many of those dances start with a step to the right?

c. It turns out that, once he started his little dance, the professor never visited his starting position anymore. How many different possibilities are there now for professor K’s dance?

**Problem #4 of the 2019 MMM: Cards in space**

Lando bets his spaceship against Han in a party of the most famous card game in the universe. We shuffle 24 cards, numbered from 1 to 24, then we deal half of the cards to Lando and half of the cards to Han. One at a time, they play one of their cards on the table, with the number visible. The winner is the first player who plays a card such that the sum of the cards on the table is divisible by 25. If Lando starts, and if each player plays optimally, what is the probability that Han wins (and then becomes the new owner of the Millenium Falcon)?

More problems and solutions, as well as the results and photos of previous years, contact details and other information, can be found on the website of the Mathematical Modeling Competition Maastricht.