2023年12月20日发(作者：小学数学试卷哪里的最难)

PROBLEM A: The Keep-Right-Except-To-Pass Rule The Keep-Right-Except-To-Pass RuleIn countries where driving automobiles on the right is the rule

(that is, USA, China and most other countries except for Great

Britain, Australia, and some former British colonies), multi-lane

a rule that requires drivers to drive in freeways often employthe right-most lane unless they are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel  and analyze a mathematical model to analyze the

performance of this rule in light and heavy traffic. You may wish

to examine tradeoffs between traffic flow and safety, the role of

under- or over-posted speed limits (that is, speed limits that are

too low or too high), and/or other factors that may not be

explicitly called out in this problem statement. Is this rule

effective in promoting better traffic flow? If not, suggest and

analyze alternatives (to include possibly no rule of this kind at all)

that might promote greater traffic flow, safety, and/or other

factors that you deem countries where driving automobiles on the left is the norm,

argue whether or not your solution can be carried over with a

simple change of orientation, or would additional requirements

be , the rule as stated above relies upon human judgment for

compliance. If vehicle transportation on the same roadway was

fully under the control of an intelligent system – either part of

the road network or imbedded in the design of all vehicles using

the roadway – to what extent would this change the results of

your earlier analysis?问题A：除非超车否则靠右行驶的交通规则

在一些汽车靠右行驶的国家（比如美国，中国等等），多车道的高速公路常常遵循以下原则：司机必须在最右侧驾驶，除非他们正在超车，超车时必须先移到左侧车道在超车后再返回。

建立数学模型来分析这条规则在低负荷和高负荷状态下的交通路况的表现。你不妨考察一下流量和安全的权衡问题,或你不妨考察一下流量和安全的权衡问题,车速过高过低的限制，者这个问题陈述中可能出现的其他因素。这条规则在提升车流量的方面是否有效？如果不是，提出能够提升车流量、安全系数或其他因素的替是否有效？如果不是，提出能够提升车流量、安全系数或其他因素的替代品（包括完全没有这种规律）并加以分析。

在一些国家，汽车靠左形式是常态，探讨你的解决方案是否稍作修改即可适用，或者需要一些额外的需要。最后，以上规则依赖于人的判断，如果相同规则的交通运输完全在智能系统的控制下，无论是部分网络还是嵌入使用的车辆的设计，在何种程度上会修改你前面的结果？

PROBLEM B: College Coaching LegendsSports Illustrated, a magazine for sports enthusiasts, is looking

for the “best all time college coach” male or female for the

previous century. Build a mathematical model to choose

bestthe

college coach or coaches (past or present) from among either

male or female coaches in such sports as college hockey or field

hockey, football, baseball or softball, basketball, or soccer. Does

it make a difference which time line horizon that you use in your

analysis, i.e., does coaching in 1913 differ from coaching in 2013?

Clearly articulate your metrics for assessment. Discuss how your

model can be applied in general across both genders and all

possible sports. Present your model’s top 5 coaches in each of

3 different sports.

In addition to the MCM format and requirements, prepare a 1-2

page article for

Sports Illustrated that explains your results and

includes a non-technical explanation of your mathematical

model thatsports fans will understand.问题B：大学传奇教练

体育画报是一个为运动爱好者服务的杂志，正在寻找在整个上个世纪的“史上最好的大学教练”。建立数学模型选择大学中在一下体育项目

中最好的教练：曲棍球或场地曲棍球，足球，棒球或垒球，篮球，足球。

时间轴在你的分析中是否会有影响？比如1913时间轴在你的分析中是否会有影响？比如1913年的教练和1913年的教练和2013年的教练和2013年的2013年的

教练是否会有所不同？清晰的对你的指标进行评估，讨论一下你的模型应用在跨越性别和所有可能对的体育项目中的效果。展示你的模型中的在三种不同体育项目中的前五名教练。

除了传统的MCM格式，准备一个1格式，准备一个1到2页的文章给体育画报，解释你的结果和包括一个体育迷都明白的数学模型的非技术性解释。


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