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# 2007 Contest

A total of 949 teams registered for the 2007 Mathematical Contest in Modeling. Each team had to chose one of three problems (Problem A, B, or C) which they would attempt to solve during the second weekend of February. Teams from all over the world competed in this contest.

A total of 1222 teams successfully completed the contest earning the following possible designations (from highest to lowest): Outstanding, Meritorious, Honorable Mention, and Successful Participant. All of the competing teams are to be congratulated for their excellent work and enthusiasm for scientific and mathematical modeling and interdisciplinary problem solving.

Problems A and B constitute the MCM (Mathematical Contest in Modeling) and Problem C constitutes the Interdisciplinary Contest in Modeling (ICM). Below are the statistics for the MCM and ICM.

## Team Omega - MCM Problem A Successful Participant

• Andrew McFayden, Freshman - Mathematics w/ Music Minor
• Michael Souza, Sophomore, CS w/ Mathematics Minor
• Ashley Swandby, Junior - Mathematics

## Team Theta - MCM Problem A Successful Participant

• Kimberly Bowman, Senior - Mathematics
• Zach Johnson, Junior - Mathematics w/ CS Minor
• Brandon Taylor, Senior - Mathematics

• Dr. M. Leigh Lunsford

## The Problems

### PROBLEM A: Gerrymandering

The United States Constitution provides that the House of Representatives shall be composed of some number (currently 435) of individuals who are elected from each state in proportion to the state's population relative to that of the country as a whole. While this provides a way of determining how many representatives each state will have, it says nothing about how the district represented by a particular representative shall be determined geographically. This oversight has led to egregious (at least some people think so, usually not the incumbent) district shapes that look "unnatural" by some standards.

Hence the following question: Suppose you were given the opportunity to draw congressional districts for a state. How would you do so as a purely "baseline" exercise to create the "simplest" shapes for all the districts in a state? The rules include only that each district in the state must contain the same population. The definition of "simple" is up to you; but you need to make a convincing argument to voters in the state that your solution is fair. As an application of your method, draw geographically simple congressional districts for the state of New York.

### PROBLEM B: Wheel Chair Access at Airports

Airlines are free to seat passengers waiting to board an aircraft in any order whatsoever. It has become customary to seat passengers with special needs first, followed by first-class passengers (who sit at the front of the plane). Then coach and business-class passengers are seated by groups of rows, beginning with the row at the back of the plane and proceeding forward.

Apart from consideration of the passengers' wait time, from the airline's point of view, time is money, and boarding time is best minimized. The plane makes money for the airline only when it is in motion, and long boarding times limit the number of trips that a plane can make in a day.

The development of larger planes, such as the Airbus A380 (800 passengers), accentuate the problem of minimizing boarding (and deboarding) time.

Devise and compare procedures for boarding and deboarding planes with varying numbers of passengers: small (85-210), midsize (210-330), and large (450-800).

Prepare an executive summary, not to exceed two single-spaced pages, in which you set out your conclusions to an audience of airline executives, gate agents, and flight crews.

An article appeared in the NY Times Nov 14, 2006 addressing procedures currently being followed and the importance to the airline of finding better solutions. The article can be seen at: http://travel2.nytimes.com/2006/11/14/business/14boarding.html (archived version)

### PROBLEM C: Organ Transplant: The Kidney Exchange Problem

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## Overall Results

A total of 949 teams registered for the 2007 Mathematical Contest in Modeling. Each team had to chose one of three problems (Problem A, B, or C) which they would attempt to solve during the second weekend of February. Teams from all over the world competed in this contest. A total of 1222 teams successfully completed the contest earning the following possible designations (from highest to lowest): Outstanding, Meritorious, Honorable Mention, and Successful Participant. All of the competing teams are to be congratulated for their excellent work and enthusiasm for scientific and mathematical modeling and interdisciplinary problem solving.

Problems A and B constitute the MCM (Mathematical Contest in Modeling) and Problem C constitutes the Interdisciplinary Contest in Modeling (ICM). Below are the statistics for the MCM and ICM.

Classification MCM (Problems A and B) ICM (Problem C)
Total Number of Participating Teams 949 273
High School Teams 13 (1%) 2 (1%)
United States Teams 283  (30%) 36 (13%)
Foreign Teams form Australia, Canada, China, England, Finland, Indonesia, Ireland, Jamaica, Korea, New Zealand, Singapore, and South Africa 666 (70%) 233 (87%)
Outstanding Winners 14 (1%) 4  (2%)
Meritorious Winners 122 (13%) 42 (16%)
Honorable Mentions 255 (27%) 169 (61%)
Successful Participants 558 (59%) 58 (21%)

## Virginia Schools

• James Madison University, Harrisonburg, David B Walton, Problem A, Meritorious
• University of Richmond, Richmond, Kathy W Hoke, Problem A, Meritorious
• Godwin High School Science, Mathematics, and Technology Center, Richmond, Ann W Sebrel, Problem B, Honorable Mention
• James Madison University, Harrisonburg, Anthony Tongen, Problem B, Honorable Mention
• Maggie Walker Governor's School, Richmond, John A. Barnes, Problem B, Honorable Mention
• Maggie Walker Governor's School, Richmond, John A. Barnes, Problem B, Honorable Mention
• Godwin High School Science, Mathematics, and Technology Center, Richmond, Ann W Sebrell, Problem C, Honorable Mention
• James Madison University, Harrisonburg, Anthony Tongen, Problem C, Honorable Mention
• James Madison University, Harrisonburg, Hasan N Hamdan, Problem C, Honorable Mention
• Maggie Walker Governor's School,Richmond, Harold Houghton, Problem C, Honorable Mention
• Eastern Mennonite University, Harrisonburg, Leah Shao Boyer, Problem A, Successful Participant
• Eastern Mennonite University, Harrisonburg, Leah Shao Boyer, Problem A, Successful Participant
• Longwood University, Farmville, M. Leigh Lunsford, Problem A, Successful Participant
• Longwood University, Farmville, M. Leigh Lunsford, Problem A, Successful Participant
• Virginia Western Community College, Roanoke, Steve T Hammer, Problem A, Successful Participant
• Maggie Walker Governor's School, Richmond, Harold Houghton, Problem B, Successful Participant