Sample Problems

Provided here are several examples of the type of problem you may be asked to solve during your M3 Challenge.

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 also 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 2015 Problem

Please note that the papers posted here are the solutions of the top six finishing teams in the 2015 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 (Summa Cum Laude Team Prize) [650K PDF]

M3 Challenge Runner Up (Magna Cum Laude Team Prize) [710K PDF]

MChallenge Third Place (Cum Laude Team Prize) [990K PDF]

MChallenge Fourth Place (Meritorious Team Prize) [690K PDF]

MChallenge Fifth Place (Exemplary Team Prize) [300K PDF]

MChallenge Sixth Place (First Honorable Mention Team Prize) [290K PDF]

past problems

Go to the M3 Challenge archive to see the:

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]

and their solutions.

Additional Resources

Teacher-Coach Guides

Teacher guides for some of the earlier Challenges can be found in those years' archive Challenge Flyers & Docs section and may not be reflective of current Challenge parameters.