Sample Problems

Featured Practice Problems

Check out the 2017 Challenge Problem: From Sea to Shining Sea: Looking Ahead with the National Park Service.

Chat with the Problem Author Dr. Neil Nicholson on Monday, March 13 2:30-4:00pm EST! 

Post your questions, ideas for starting, or solutions about the problem at any time for feedback in the "Comments" section below the problem.


Modeling Scenarios: Levels 1, 2, and 3  

Several examples of the types of problems you may be asked to solve in the M3 Challenge are presented here.

It is highly recommended that participants read and work through some problems at each level before moving on


Level 1:

Modeling Scenarios [14K PDF]

This list is intended to give students a taste of some of the scenarios that may be presented as modeling problems in the M3 Challenge. This can be considered basic training material, designed to prompt targeted brainstorming.

List provided courtesy of William P. Fox, Department of Mathematics, Francis Marion University, Florence, SC.

Level 2: AIM Resource Books


A Backwater Curve for the Windsor Locks Canal [1.09MB PDF]

Budgeting Time and Money [382K PDF]

Pricing Auto Insurance [466K PDF]

Volcanic Eruption Fallout [560K PDF]


A Backwater Curve for the Windsor Locks Canal [1.73MB PDF]

Budgeting Time and Money [1.8MB PDF]

Pricing Auto Insurance [1.7MB PDF]

Volcanic Eruption Fallout [1.5MB PDF]

These booklets detail modeling problems that remain relevant today despite being somewhat dated in appearance. These examples have considerable background data, which gives insight into the types of details that need to be considered when solving the Challenge problem. Remember that creativity and originality are highly valued characteristics of a winning solution—along with good quantitative and qualitative analysis.

Used with the permission of the Mathematical Association of America.

Level 3: M3 Challenge Archives: Past Problems and Outstanding Solution Papers

M3 Challenge 2016 Problem

Please note that the papers posted here are the solutions of the top six teams in the 2016 M3 Challenge. The students completed these papers within the 14-hour time period allowed for the contest and were selected by the judges to receive an award.

M3 Challenge Champions - St. John's School

M3 Challenge First Runner Up - Carmel High School

MChallenge Third Place - Governor Livingston High School

MChallenge Finalist - La Salle Academy

MChallenge Finalist - Montgomery Blair High School

MChallenge Finalist - North Carolina School of Science and Mathematics

Past Problems

2015 Problem [230K PDF]

2014 Problem [317K PDF]

2013 Problem [317K PDF]

2012 Problem [244K PDF]

2011 Problem [273K PDF]

2010 Problem [60K PDF]

2009 Problem [103K PDF]

2008 Problem [258K PDF]

2007 Problem [258K PDF]

2006 Problem [203K PDF]

Go to the M3 Challenge archive to see these problems and their solutions.