4 February 2019

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.

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?

Solution

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)?

Solution

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.