Math Modeling Contests

Math Modeling Contests

Mathematical Modeling

The Mathematical Contest in Modeling (MCM) and its sister contest, the Interdisciplinary Contest in Modeling (ICM), provide great opportunities for students to focus on problem solving skills in a real-world environment. Problems come from research areas of applied mathematics related to many fields – business, environmental sciences, and sports are a few examples. Student teams are given 96 hours to analyze a single open ended problem, develop a model of the problem, solve the model, and write a report. Carroll’s faculty meet with student teams weekly in the months before the competition to help them prepare for the unique nature of this international contest. Find out more about MCM/ICM

Carroll College Excels

Carroll has had three teams awarded the contest's highest ranking: In 2003, Carroll's ICM team of Kylan Johnson, Gary Olson, and Joe Rasca was awarded an Outstanding Winner ranking. In 2006, Carroll's MCM team of Ben Dunham, Kyle Nixon, and Steffan Francischetti was awarded an Outstanding Winner ranking, placing them in the elite company of Cal Tech, Harvey Mudd, MIT, and Harvard. In 2010, the MCM team of Brittany Harris, Chase Peaslee, and Kyle Perkins were one of 4 Outstanding teams along with Beijing Jiaotong University, Hangzhou Dianzi University, and Lawrence University.

In 2021, the MCM team of Sabrina Crooks, Shirley Davidson, and Madeline Norton placed within the top 3% of participants worldwide with a "Finalist" designation. Only eight U.S. teams earned ranks of "Finalist" or better in the competition. 

Montana Mathematical Modeling Challenge (MMMC)

The Montana Mathematical Modeling Challenge (MMMC) is an intense, 24 hour contest for undergraduate students. Teams are presented with two open ended, real world problems and have one day to choose and solve one of them using any non-sentient resources they can find. Find out more about MMMC

Montana Math Modeling Challenge (MMMC)

MMMC Frequently Asked Questions

The Montana Math Modeling Challenge (MMMC) is a 24-hour regional modeling contest for undergraduate students. In 2008, the University of Iowa hosted the first such regional contest, (called the Midwest Mathematical Modeling Competition, or MMMC), which involved 13 teams from 5 different schools.  Since then, dozens of schools have hosted these 24-hour Mathematical Modeling Challenges.  This year's contest will be the fifth time that Carroll has hosted the MMMC.

Feedback and interaction. The MMMC is designed to provide students with multiple forms of immediate feedback on their solutions. Additionally as an on-site contest, student participants have the opportunity to interact with peers from other institutions as well as observe different solution approaches presented by other teams. In brief, the MMMC differs from other contests in the following ways:

  1. All student teams work on their solutions at a regional host site.
  2. Teams have only 24 hours to prepare a solution to one of the given problems.
  3. Each team prepares a brief oral presentation of their model and a one-page summary of their results.
  4. An advisory panel reviews and provides feedback for summaries; students peer-review the oral presentations.

Yes. Teams of students from first-year through fourth-year with varying mathematical backgrounds have all successfully developed solutions. Please take a look at a few question sets and solutions from past contests as a gauge of question difficulty.

Question sets:

MMMC Contest Rules

Contest Rules

Participants in the MMMC are expected to follow the spirit of the rules used by COMAP in the MCM/ICM contests. Most notably, students will be bound by the following two rules:

  1. Teams may use any inanimate source of data or materials --- computers, software, references, web sites, books, etc., however all sources used must be credited. Failure to credit a source will result in a team being disqualified from the competition.
  2. Team members may not seek help from or discuss the problem with their advisor or anyone else, except other members of the same team. Input of any form from anyone other than student team members is strictly forbidden. This includes email, telephone contact, personal conversation, communication via web chat or other question-answer systems, or any other form of communication.

Summary Sheet

  • At the top of your summary sheet list the title and team number only. Do NOT list any group member names or institution information.
  • The summary should be no more than two pages in length and should be single spaced with a 12 point font.
  • Teams may submit an additional sheet listing the references used to create their model.

A summary should clearly describe your approach to the problem and, most prominently, what your most important conclusions were. The summary should inspire a reader to learn the details of your work.

10-Minute Presentation

  • Clearly state (in your own words) which problem you are solving and how you plan to solve it.
  • List and provide rationale for all assumptions you make in solving your problem.
  • List all variables used in your model.
  • If applicable, justify your choice of model by comparing it to other models.
  • Discuss your model's strengths and weaknesses. Use pictures, charts, diagrams, etc. to explain your problem and your solution methods.
  • Try to avoid reading text off the screen.
  • Discuss future goals and ideas concerning your problem.

The Mathematical Contest in Modeling (MCM) and Interdisciplinary Contest in Modeling (ICM)


The Mathematical Contest in Modeling (MCM) and its sister contest, the Interdisciplinary Contest in Modeling (ICM) are international competitions sponsored by COMAP that ask teams of three undergraduates to spend a weekend modeling an applied mathematics problem. These competitions provide great opportunities for students to focus on problem solving skills in a real-world environment. Problems come from research areas of applied mathematics related to many fields – business, environmental sciences, and sports are a few examples. Student teams are given 96 hours to analyze a single open ended problem, develop a model of the problem, solve the model, and write a report. Carroll’s faculty meet with student teams weekly in the months before the competition to help them prepare for the unique nature of this international contest.

COMAP's Mathematical Contest in Modeling (MCM) successfully encourages teamwork, creativity and written exposition. However, one (logistically necessary) element that many students remark is lacking from this competition is adequate feedback -- both from the micro perspective "What do the judges really think of my team's paper?" to the macro "How did other teams answer this question?" This contest was designed in response to the aforementioned student concerns and has been developed to meet the following objectives:

  • Encourage independent thinking.
  • Promote collaboration.
  • Develop mathematical communication abilities.
  • Prepare student teams to participate in the MCM.
  • Create a unique mathematical community.

HELENA – A team of Carroll College students recently ranked among the top in the world in the annual Mathematical Contest in Modeling (MCM)/Interdisciplinary Contest in Modeling (ICM) sponsored by the Consortium for Mathematics and Its Applications (COMPAP). Three Carroll College teams competed in the February competition with one team placing in the top three percent of all participants worldwide.

The MCM/ICM is a unique international contest for undergraduate students. It challenges teams of students to clarify, analyze, and propose solutions to open-ended real-world problems. Students participate as team members rather than as individuals, creating an environment for sharing knowledge and skills. Student teams are given 100 hours to analyze a single open-ended problem, develop a model of the problem, solve the model, and write a report.

This year, a total of 26,112 teams from nearly 20 countries and regions across the globe participated in the competition. Carroll College had nine students volunteer to compete in three teams of three students.

Carroll’s top-performing team was ranked as “Finalist,” placing them in the top 3% of all teams. Only eight U.S. teams earned ranks of "Finalist" or better. One Carroll team was ranked as “Honorable Mention,” placing them in top 24% of teams, and one team was ranked as “Successful Participant.”

  • MCM Problem C, Finalist:  Sabrina Crooks, Shirley Davidson, Madeline Norton
  • ICM Problem A, Honorable Mention:  Keaton Blair, Connor James, Milos Vukadinovic
  • ICM Problem A, Successful Participant:  Ethan Mancini, Iain Scott, Makenzie Jahn

Read more about the 2021 MCM/ICM teams

Carroll teams have placed in the top 1% in the MCM/ICM in 2003, 2006 and 2010. Learn more about the competition.


Carroll ICM and MCM Teams

YearStandingTeam MembersProblem
2021FinalistSabrina CrooksShirley DavidsonMadeline NortonAsian giant hornets
2021Honorable MentionKeaton BlairConnor JamesMilos VukadinoviFungi on woody fibers
2021Successful ParticipantEthan ManciniIain ScottMakenzie JahnFungi on woody fibers
2019Meritorious WinnerTerry CoxSabrina CrooksShirley DavidsonEmergency Louvre evacuation
2019Honorable MentionChase EngleDaniel GuthrieMorgan ShimkusEcological impact of dragons
2019Honorable MentionMadeline NortonMatthew SmillieAustin WassenbergCombating opioid abuse
2019Successful ParticipantKristen BresslerReina IshibashiTheresa TrinhMedical supply chains
2019Successful ParticipantRyan CainJoyce LuiMorgan ShimkusEcological impact of dragons
2018Successful ParticipantHunter BolesMackenzie JahnFrank PopeOut of Gas
2018Successful ParticipantCordell AndersenTommy LeJenny MeadowcroftOut of Gas
2018Meritorious WinnerJesica BauerNathan BooneTerry Cox Energy Production 
2018Successful ParticipantReina IshibashiTrey ScofieldAmy TelckHow many languages?
2018Honorable MentionJoseph IkeharaErica WiensElisabeth YounceHow many languages?
2018Successful ParticipantRyan CainJoyce LuiMorgan ShimkusEnergy Production
2018Successful ParticipantTorrey HoffAndrew JohnsonDaniel OlszewskiClimate Change
2017Meritorious WinnerKellen MillerGreg JonesMichael BradtThe Zambezi River
2017Honorable MentionJordan TrinkaJoseph ZepedaAnthony NunoMerge After Toll
2017Honorable MentionFrank PopeJoyce LuiMorgan ShimkusOptimizing Airport Security
2017Meritorious WinnerNathan BooneTerry CoxDylan AllenOptimizing Airport Security
2017Honorable MentionAndrew JohnsonDaniel OlszewskiBryce SamwelMigration to Mars
2017Meritorious WinnerJesica BauerErica WiensJoseph IkeharaOptimizing Airport Security
2017Successful ParticipantCristina Lopez Cordell AndersenDaniel BrantOptimizing Airport Security
2016Meritorious WinnerIbrahima NiangSubin SapkotaNick LumettaThirsty Planet
2016Meritorious WinnerChris MichaelAl OlszewskiJacob JohnsonRefugee Immigration Policies 
2016Honorable MentionMark RomanoKelby DepnerJoel Kramer Space Junk
2016Honorable MentionJesica BauerJoseph IkeharaDerek SmithSpace Junk
2016Successful ParticipantErin HansonDempsey RogersScott GullifordThe Goodgrant Challenge
2016Successful ParticipantJordan TrinkaIsabelle GrayMichael RemingtonA Hot Bath
2016Successful ParticipantAlex ChopyakRyan ArmstrongBrian HomSpace Junk
2016Successful ParticipantErica WeinsCristina LopezCordell AndersenSpace Junk
2016Successful ParticipantBen JensenHannah LerumElisabeth YounceA Hot Bath
2015Meritorious Winner Ibrahima Niang Subin Sapkota Nick LumettaEradicating Ebola
2015Meritorious Winner Mark Romano Kelby Depner Joseph ZepedaEradicating Ebola
2015Meritorious Winner Jesica Bauer Sarah Fitzpatrick Austin PowellSearching for a lost plane
2015Meritorious Winner Ryan Armstrong Ben Jensen Jake JohnsonSearching for a lost plane
2015Honorable Mention Mark Griffith Elizabeth CarlsonElizabeth SchweizerSearching for a lost plane
2015Honorable Mention Alex Chopyak Derek SmithNicole SeehaferSearching for a lost plane
2015Honorable Mention Brian Luehr Dawson Osborn Dmitri ShulgaManaging Human Capital in Organizations
2015Meritorious Winner Scott Gulliford Kaitlin Johnson Dempsey RogersIs it sustainable?
2015Honorable Mention Chris Michael Al Olszewski Tyler ZimmerIs it sustainable?
2014Honorable MentionIbrahima NiangSubin SapkotaNick LumettaCollege Coaching Legends
2014Successful ParticipantMyunghoon KimElias PomeroyTony RosalesCollege Coaching Legends
2014Successful ParticipantJoe KingJonathon KujawaRachel RiitanoCollege Coaching Legends
2014Successful ParticipantKyle GriffithTanner GustavsenMark RomanoCollege Coaching Legends
2014Successful ParticipantMark GriffithMichaela NordheimAlyssa NugentCollege Coaching Legends
2014Successful Participant Elizabeth CarlsonDempsey Rogers Kathleen Schut Keep-Right-Except-To-Pass
2013Honorable MentionSarah FitzpatrickSydney PhilippsKiersten UtseyNetwork Modeling of Earth's Health
2013Successful ParticipantJoseph KingAustin PowellRachel RiitanoWater, Water, Everywhere
2013Successful ParticipantIan KesslerCody NoffsingerColin WillettThe Ultimate Brownie Pan
2013Successful ParticipantMyunghoon KimJessica KnappNick KaideThe Ultimate Brownie Pan
2013Successful ParticipantJonathon KujawaEvan TremaineTyler WahlWater, Water, Everywhere
2013Successful ParticipantMike FioreElias PomeroyNate WoodsThe Ultimate Brownie Pan
2013Successful ParticipantRyan SwensonSabrina RhinesTarryn VavriskaThe Ultimate Brownie Pan
2013Successful ParticipantMark GriffithAlyssa NugentShawn ReagorWater, Water, Everywhere
2012Meritorious WinnerJennings AndersonBrian HurtleGrant WilliamsModeling for Crime Busting
2012Honorable MentionEmily SperanzaKiersten UtseyBill VilwockThe Leaves of a Tree
2012Honorable MentionRyan SwensonSabrina RhinesAlyssa NugentCamping along the B. L. River
2012Honorable MentionDavid ConnollyMark GriffithKyle Sturgill-SimonCamping along the B. L. River
2012Honorable MentionChris KieferBen McIsaacNatalie StewartCamping along the B. L. River
2012Honorable MentionJeff AllenSydney BronsonTaylor StewartCamping along the B. L. River
2012Honorable MentionSydney PhillippsJulia PlattColin WillettModeling for Crime Busting
2012Honorable MentionMyunghoon KimElias PomeroyKevin SemmensModeling for Crime Busting
2012Successful ParticipantBrian LuehrEvan TremaineNate WoodsCamping along the B. L. River
2011Meritorious WinnerBrittany HarrisChase PeasleeDylan WertzElectric Cars
2011Meritorious WinnerJeff AllenSydney BronsonIan LyonRepeater Coordination
2011FinalistJennings AndersonBrian HurtleGrant WilliamsElectric Cars
2011Meritorious WinnerShannon BenchAlyssa NugentAmber NuxollElectric Cars
2011Successful ParticipantScott HarmonGreg JanysekNick RyhajloRepeater Coordination
2011Successful ParticipantJoe BarstadSam SchaeferEvan TremaineSnowboard Course
2011Meritorious WinnerBen DillMyunghoon KimForrest LaskowskiRepeater Coordination
2011Honorable MentionMckenzie Keeling-GarciaRyan SwensonNate WoodsRepeater Coordination
2011Successful ParticipantElizabeth HezelKathleen O'LearyBill VilwockElectric Cars
2011Honorable MentionSydney PhilippsAmy ReagorSarah ReehlElectric Cars
2010Outstanding WinnerBrittany HarrisChase PeasleeKyle PerkinsThe Great Pacific Ocean Garbage Patch
2010Meritorious WinnerJeff AllenIan LyonNate WoodsThe Sweet Spot
2010Meritorious WinnerJennings AndersonJoe BarstadAleks NavratilThe Sweet Spot
2010Meritorious WinnerJessica ForbesJohn FosterKyle Sturgill-SimonCriminology
2010Meritorious WinnerScott HarmonGreg JanysekNick RyhajloCriminology
2010Honorable MentionShane GalloglyJen MajerusDylan WerstCriminology
2010Honorable MentionGreg BeasleyBen DillRyan SwensonCriminology
2010Honorable MentionColin BradleyMickey DohertyAmy ReagorCriminology
2010Successful ParticipantShannon BenchSleight HalleyChris KieferThe Sweet Spot
2010Successful ParticipantJeremy HovdenBrandon LayesStan McLennaThe Sweet Spot
2010Successful ParticipantJohn GreffNicklas HavensSam SchaeferThe Sweet Spot
2010Successful ParticipantGarrett BarnesFluvio LoboJonathan RainwaterThe Sweet Spot
2009Meritorious WinnerJohn GreffNicklas HavensSam SchaeferDesigning a Traffic Circle
2009Meritorious WinnerScott HarmonAleks NavratilNick RyhajloDesigning a Traffic Circle
2009Meritorious WinnerAndrew CifalaJeremy HovdenDylan WerstEnergy and the Cell Phone
2009Meritorious WinnerBen DunhamElise KloheIan LyonCreating Food Systems
2009Honorable MentionAdrian ConleyBrandon LayesStanley McLennaEnergy and the Cell Phone
2009Honorable MentionCarl BernstenBen IsraelGarrett ThompsonEnergy and the Cell Phone
2009Successful ParticipantDustin DickersonBen DillJessica ForbesDesigning a Traffic Circle
2009Successful ParticipantAdam BrockwayBrittnay HarrisKelsey HuntDesigning a Traffic Circle
2009Successful ParticipantJennings AndersonGreg BeasleyCassie RapkochDesigning a Traffic Circle
2009Successful ParticipantJohn FosterKatie SemmensKyle Sturgill-SimonEnergy and the Cell Phone
2009Successful ParticipantAJ AllenAndrew MendezSean SweeneyEnergy and the Cell Phone
2008Honorable MentionBen DunhamSteffan FrancischettiAntony SperanzaSudoku Problem
2008Successful ParticipantChris CasebeerKate DramstadElise KloheHealthcare Systems
2008Successful ParticipantPam BennettClaire GilbertsonKelsey HuntHealthcare Systems
2008Meritorious WinnerJohn FosterJohn RiggsPaul VanValkenburgSudoku Problem
2008Successful ParticipantGreg BeasleyDustin DickersonErica WoodTake a Bath
2008Honorable MentionCarl BernstenBen IsraelGarrett ThompsonTake a Bath
2008Honorable MentionShawn AndersenIan LyonCassie RapkochHealthcare Systems
2007Meritorious WinnerBen DunhamSteffan FrancischettiKyle NixonGerrymandering
2007Honorable MentionElise KloheHolly PerrymanGreg RayAirplane Seating
2007Honorable MentionPam BennettEmerson GodboltJimmie HyunOrgan Transplant
2007Successful ParticipantDustin DickersonJoe O'ConnorJohn RiggsOrgan Transplant
2007Meritorious WinnerAnthony RascaAntony SperanzaErica WoodGerrymandering
2007Meritorious WinnerCarl BernstenNeil HartGarrett ThompsonAirplane Seating
2007Honorable MentionShawn AndersenGreg BeasleyBen IsraelOrgan Transplant
2006Outstanding WinnerBen DunhamSteffan FrancischettiKyle NixonSprinkler Systems
2006Meritorious WinnerElise KloheHolly PerrymanGreg RaySprinkler Systems
2006Honorable MentionPam BennettJeremy DeterJimmie HyunSprinkler Systems
2006Successful ParticipantShane GarrickJohn RiggsPaul VanValkenburgHIV/AIDs Modeling
2006Meritorious WinnerAlaina GarciaAnthony RascaYing ZhuHIV/AIDs Modeling
2006Honorable MentionSarah HartensteinLucas MeuchelBrahms ZepedaHIV/AIDs Modeling
2005Meritorious WinnerJohn FowlerKyle NixonSheena StrohmayerFlood Planning
2005Successful ParticipantAlaina GarciaGreg RayJoshua SykesNonrenewable Resources
2005Successful ParticipantJeff LarsonJohn RiggsPablo VanWoerkomTollbooths
2005Honorable MentionJeremy DeterGeorge MetzgerJeff MichelsonNonrenewable Resources
2005Honorable MentionShane GarrickAnthony RascaYing ZhuTollbooths
2005Successful ParticipantPam BennettSeth DeLongBen DunhamTollbooths
Honorable MentionKelly BeffertLoren BrownSarah HartensteinTo Be Secure or Not to Be?
2004Meritorious WinnerJohn LouieAnthony RascaJoshua SykesTo Be Secure or Not to Be?
2004Honorable MentionJessica DavisLucas MeuchelJeffrey MichelsonTo Be Secure or Not to Be?
2004Honorable MentionJohn FowlerShane GarrickJoseph RascaQuickPass
2004Meritorious WinnerSeth DeLongGeorge MetzgerShannon O'BrienQuickPass
2004Honorable MentionJoseph HavensPablo VanWoerkomYing ZhuQuickPass
2004Successful ParticipantJeff LarsonAdam NielsenGreg RayFingerprints
2003 picsOutstanding WinnerKylan JohnsonGary OlsonJoseph RascaAirport Screening
2003Honorable MentionJohn FowlerShane GarrickLevi MielkeAirport Screening
2003Honorable MentionRogie KingJohn LouieAmelia ValasekAirport Screening
2003Honorable MentionTom BaillyShannon O'BrienBrett PennerStunt Person
2002 picsMeritoriousLindsay BlackLevi MielkeGary OlsonScrub Lizards
2002Honorable MentionKelly BeffertJohn FowlerTed WendtWind and Waterspray
2002Honorable MentionJessica DavisKylan JohnsonShannon O'BrienAirline Overbooking
2001 picsHonorable MentionToshie MatsuokaJennifer StewartTed WendtZebra Mussels
2001Successful ParticipantAmanda BlackburnJoe HayterMatt ZantoBicycle Wheel
2001Successful ParticipantRebecca BakerGary OlsonSean TannerBicycle Wheel
2001Successful ParticipantMichelle KennedyJaime KopfCassi ShelleyHurricane Evacuation

Past results


2021 Math Modeling

We are incredibly proud to share that one of our teams placed in the top 3% of all teams worldwide in their category – Carroll's highest finish in 11 years! Only eight U.S. teams earned ranks of "Finalist" or better! Read more about it

2021 Finalist Team (L to R): Madeline Norton, Shirley Davidson, Sabrina Crooks

Math Graduates

2010 Math Modeling Contest

For the 3rd time in the last 7 years, we had an Outstanding Winner team!  See the Helena Independent Record article on Carroll's winning team!

INFORMS Outstanding Winner Team: Brittany Harris, Kyle Perkins, Chase Peaslee
2010 MCM Team

Schweitzer and 2010 Math
From left: Chase Peaslee, Montana Governor Brian Schweitzer, and Brittany Harris

2006 Math Modeling

The team of Kyle Nixon, Steffan Francischetti, and Ben Dunham received a ranking of OUTSTANDING in the Mathematical Contest in Modeling! This places them in the top 1% worldwide, and in the company of Harvard, MIT, Duke, Rice, RPI, CU-Boulder, UC-Davis, and 2 teams from China. 

Here are the results from the 2006 Contest:

Outstanding Winners:
* Kyle Nixon - Junior Civil Engineering major (Helena)
* Ben Dunham - Sophomore Math and Computer Science major (Clancy)
* Steffan Francischetti - Sophomore Mathematics/Engineering major (Billings)

2006 Math team
From left: Ben Dunham, Steffan Francischetti, and Kyle Nixon

Math Modeling 2
From left: Ben Dunham, Dr. Holly Zullo, Montana Governor Brian Schweitzer,
Steffan Francischetti, Kyle Nixon, Dr. Mark Parker, and Carroll President Dr. Thomas Trebon

Math Modeling 2006 Math Modeling 2006-2

The three Outstanding Winners and Dr. Trebon chat with Governor Schweitzer.