# Mathematical Contest in Modeling, 2008

## The event

The Mathematical Contest in Modeling is an annual event, sponsored by the Consortium for Mathematics and Its Applications, in which students at colleges and universities all over the world are asked to develop and analyze mathematical models of open-ended, practical problems for which no direct solutions are known. Participants work in teams of three and are permitted to use libraries, computers, and other inanimate sources of knowledge and inspiration. The organizers of the contest propose three problems; over the four days of the contest, each team selects one of these problems, designs, implements, and analyzes a model, and writes a substantial report presenting its results.

The twenty-third Mathematical Contest in Modeling was held on February 14-18, 2008. Grinnell fielded one team this year:

• Pengjun Shen 2011, Yusheng Xie 2011, and Jiabei Pan (faculty sponsor: Karen Shuman)

## The problems

Here are the problems that COMAP posed this year. Our team elected to work on Problem A.

### Problem A: Take a bath

Consider the effects on land from the melting of the north polar ice cap due to the predicted increase in global temperatures. Specifically, model the effects on the coast of Florida every ten years for the next 50 years due to the melting, with particular attention given to large metropolitan areas. Propose appropriate responses to deal with this. A careful discussion of the data used is an important part of the answer.

### Problem B: Creating Sudoku puzzles

Develop an algorithm to construct Sudoku puzzles of varying difficulty. Develop metrics to define a difficulty level. The algorithm and metrics should be extensible to a varying number of difficulty levels. You should illustrate the algorithm with at least 4 difficulty levels. Your algorithm should guarantee a unique solution. Analyze the complexity of your algorithm. Your objective should be to minimize the complexity of the algorithm and meet the above requirements.

## Results

This year, 1162 teams participated. Nine of these entries were judged Outstanding; 161 others, Meritorious. 478 received Honorable Mentions in COMAP's report. 512 were classified as Successful Participants and two as Unsuccessful Participants.

Grinnell's team received the Honorable Mention ranking.

This document is available on the World Wide Web as

```http://www.math.grinnell.edu/mcm-2008.xhtml
```