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通讯CUMCM Newsletter 全国大学生数学建模 竞赛组织委员会主办 创新意识 团队精神 重在参与 公平竞争 目录2007 年美国大学生数学建模竞赛(MCM) 和交叉学科建模竞赛(ICM)赛题…1) 我国学生参加

2007 年美国大学生数学建模竞赛(MCM) 和交叉学科建模竞赛(ICM)情况简介…7) 全国研究生数学建模扬州研讨会纪要…11)

2007 年天津市数学建模骨干教师培训会议议程纪要…………(12) 东北三省数学建模联赛介绍…12) 苏北数学建模联赛…13) 西北工业大学校内数学建模竞赛通讯…14) 各地数学建模竞赛试题选编…15) 第10 届全国数学建模教学和应用会议 提交分组报告截止时间延期的通知…17) 第15 届国际数学建模教学和应用会议 申办通知…………(17) 《全国大学生数学建模竞赛通讯》征稿启事…………………(17) 数学软件信息 (广告) 封底) 《全国大学生数学建模竞赛通讯》2007 年第

2 期(2007 年6月, 总第

24 期) 主办:全国大学生数学建模竞赛组织委员会 地址:北京清华大学数学科学系(邮编:100084)

网址:http://mcm.

edu.cn

电话:010-62781785 传真:010-62773400 责任编辑:唐云

1 2007 年美国大学生数学建模竞赛(MCM) 和交叉学科建模竞赛(ICM)赛题 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. A 题:不公正的选区划分 美国宪法规定众议院由一定数目的众议员(目前是

435 人)组成,他们是由各州按照该州人口占 全国总人口的百分比选出来的.尽管这种规定提供了确定每个州有多少众议员的方法,但是一点也 没有说及有关一个特定的众议员所代表的选区应该怎样按地区决定的问题.这种疏忽已经导致了按 某种标准看来是违反常情的很不好的(至少某些人认为通常是不必这样做的) 选区安排. 因此就向你们提出了以下的问题:假设你们有机会去制定一个州的众议院的选区.你们会怎样 把它作为一种纯 基础性 的练习来创建一个州的所有选区的 最简单 的划分.这些划分规则中 至少要包含一条:该州的每个选区必须有同样的人口. 简单 的定义要由你们来下;

但是你们必 须就你们的解决方法是公正的做出一个能够使该州选民信服的论证.作为你们的方法的应用,试创 建纽约州的按地域来说是简单的选区划分. PROBLEM B: The Airplane Seating Problem 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'