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South African Mathematical Modeling Contest (SAMMC)

Contest outline and instructions

Outline: The main aim of SAMMC ("Sam-see") is to provide South African undergraduate students in science and engineering disciplines some exposure to applied mathematics problems more relevant to real-world applications than they might otherwise encounter in the classroom. It is a chance to challenge their brain and develop problem-solving skills, gain experience in working in a team, and possibly win some prizes!

The format of the contest is loosely based on the international COMAP MCM competition, held every January/February: http://www.comap.com/undergraduate/contests. A secondary aim of SAMMC is to gain experience in solving MCM-type problems and to help select teams for the international competition.

More details can be found in the here and a more precise formulation of the contest rules here.

Registration

Teams from any South African University of higher education system are welcome to compete. Registration for the 2019 contest will be announced in early 2019.

SAMMC2018 Contest Report

SAMMC2018 had 7 teams from 4 universities successfully complet the contest. Of these 7 teams, 1 chose problem A (zip line), 4 chose problem B (stop-go) and 2 chose problem C (home field advantage). The final submissions were filtered by the local and contest organisers, and the final results determined by an independent adjudicator.

The following teams were successful participants:
  • Gareth Andrews, Chelsea Jessiman, Dylan Phelps (NMU)
  • Aphiwe Magaya, Sitembiso Caleni, Sizwe Sibanyoni, Matlhogonolo Manye (NMU)
  • Darrian Marais, Ogulcan Kusluoglu (Stellenbosch)
  • Boikhutso Ramanyane, Kevin Kamukapa, Kristen Smith (UP)
In joint second place
  • Team Heffalump - Adriaan de Clercq, Janco Krause (UP)
  • Team Globo gym purple cobras - Tamlin Love, Roy Gusinow, Omer Elgoni, Leeson Govender (WITS)
In first place:
  • Team SU1 - Christiaan van der Merwe, Dario Trinchero, Jeroen Bormans (Stellenbosch)

SAMMC2018 problems

SAMMC2018 Problem A: Zip it! In a bid to counter dropping tourism following recent droughts, the city of Cape Town is considering the installation an aerial zip line from the top of Table Mountain to either the top of the nearby Lion's Head or Signal Hill, or a maybe even a "splash down" landing in to the water off of Camps Bay beach. You have been contracted develop a suitable mathematical model of the proposed zip line(s), to assess the feasibility of the project, and give recommendations on its design. (An engineer has been contracted to consider most of the construction details.)

As part of your final report you should include:
  • a one-page summary for the Mayor of Cape Town
  • a short advertisement for a local paper

SAMMC2018 Problem B: STOP, wait, ..., GO! A busy two-way highway is reduced to a single lane via STOP-GO boards for a distance of L kilometres. Determine an optimal strategy (for example, in terms of the waiting time T, the number of queuing cars Q, or some combination of both) for when to change the direction of traffic in order to minimise delays.

As part of your final report you should include:
  • a one-page summary for the provincial Minister of Transport and Public Works
  • a roadside billboard explaining your strategy to waiting motorists
Possible extensions:
  • consider the case of a sequence of STOP-GOs
  • consider the case of a three-way STOP-GO (e.g.,, where there is a T-junction within the closed section.)

SAMMC2018 Problem C: Home field advantage In many sports the idea of "home field advantage" describes the potential benefit a home team gets over the away team. The advantages may be physical (for example, differing climates or weather conditions, different pitch sizes, or fatigue from travel) or psychological (typically due to increased support from fans). There has been much debate recently over the effect of home field advantage in Super Rugby (particularly with the introduction of teams from Argentina and Japan). The CEO of Super Rugby has hired you to quantify the effect this has on the competition, and possibly suggest some remedies (such as introducing a bonus point for an away win or draw).

As part of your final report you should include:
  • a one-page lay summary to the CEO of Super Rugby explaining your findings.
Historical Super Rugby results and standings can be found here.

Older problems

A collection of problems from previous problems can be found here.