Smith has competed in this annually, it is a great experience. In some recent years we have even had two teams.
This is not an individual competition; the contestants are teams. In 1999, there were 291 U.S. teams (61%) and 187 international teams (39%) successfully submitting solutions for the Contest. At the start of the contest (sometime in February, usually) teams are presented with two problems, one generally combinatorial, the other more analytic. Each team chooses one to work on. The problems are open-ended and are ``` not likely to have a unique solution.'' Teams have a full weekend to work on them, and they may use computers, libraries, or any inanimate source. By Monday afternoon, each team has prepared a typed report of their work which is then submitted.
The following is a problem taken from the 1987 contest:
The owner of a pavedThe following are from the 1999 contest:by
, corner parking lot in a New England town hires you to design the layout, that is, to design how the ``lines are to be painted.'' You realize that squeezing as many cars into the lot as possible leads to right-angle parking with the cars aligned side by side. However, inexperienced drivers have difficulty parking their cars this way, which can give rise to expensive insurance claims. To reduce the likelihood of damage to parked vehicles, the owner might then have to hire expert drivers for ``valet parking.'' On the other hand, most drivers seem to have little difficulty in parking in one attempt if there is a large enough ``turning radius'' from the access lane. Of course, the wider the access lane, the fewer cars can be accommodated in the lot, leading to less revenue for the parking lot owner.
Problem A - Deep Impact
For some time, the National Aeronautics and Space Administration (NASA) has been considering the consequences of a large asteroid impact on the earth.
As part of this effort, your team has been asked to consider the effects of such an impact were the asteroid to land in Antarctica. There are concerns that an impact there could have considerably different consequences than one striking elsewhere on the planet.
You are to assume that an asteroid is on the order of 1000 m in diameter, and that it strikes the Antarctic continent directly at the South Pole.
Your team has been asked to provide an assessment of the impact of such an asteroid. In particular, NASA would like an estimate of the amount and location of likely human casualties from this impact, an estimate of the damage done to the food production regions in the oceans of the southern hemisphere, and an estimate of possible coastal flooding caused by large-scale melting of the Antarctic polar ice sheet.
Problem B - Unlawful Assembly
Many public facilities have signs in rooms used for public gatherings which state that it is `` unlawful" for the rooms to be occupied by more than a specified number of people. Presumably, this number is based on the speed with which people in the room could be evacuated from the room's exits in case of an emergency. Similarly, elevators and other facilities often have `` maximum capacities" posted.
Develop a mathematical model for deciding what number to post on such a sign as being the `` lawful capacity". As part of your solution discuss criteria, other than public safety in the case of a fire or other emergency, that might govern the number of people considered `` unlawful" to occupy the room (or space). Also, for the model that you construct, consider the differences between a room with movable furniture such as a cafeteria (with tables and chairs), a gymnasium, a public swimming pool, and a lecture hall with a pattern of rows and aisles. You may wish to compare and contrast what might be done for a variety of different environments: elevator, lecture hall, swimming pool, cafeteria, or gymnasium. Gatherings such as rock concerts and soccer tournaments may present special conditions.
Apply your model to one or more public facilities at your institution (or neighboring town). Compare your results with the stated capacity, if one is posted. If used, your model is likely to be challenged by parties with interests in increasing the capacity. Write an article for the local newspaper defending your analysis.
Several teams have been awarded Honorable Mention: the team of Dianna Xu '96 and Junheng Luo '96 in 1993, the team of Bilge Bahar '97, Sarah Lonberg-Lew '98, and Kathy Schnare '96 in 1996, and the team of Kristina Closser '07, Juan Li '07 and Min Zheng '08 in 2005.
If you are interested, contact Ruth Haas; she will act as this year's faculty sponsor and will put together teams.