2011 MCM/ICM Problems
Mao Ziyang
IMPORTANT CHANGE TO CONTEST RULES FOR MCM/ICM 2011:
Teams (Student or Advisor) are now required to submit an electronic copy of their solution paper by email to solu...@comap.com. Your email MUST be received at COMAP by the submission deadline of 8:00 PM EST, February 14, 2011.
COMAP Mirror Site: For more in:
http://www.comap.com/undergraduate/contests/mcm/
MCM: The Mathematical Contest in Modeling
ICM: The Interdisciplinary Contest in Modeling
2011 Contest Problems
MCM PROBLEMS
Determine the shape of a snowboard course (currently known as a “halfpipe”) to maximize the
production of “vertical air” by a skilled snowboarder.
"Vertical air" is the maximum vertical distance above the edge of the halfpipe.
Tailor the shape to optimize other possible requirements, such as maximum twist in the air.
What tradeoffs may be required to develop a “practical” course?
PROBLEM B: Repeater Coordination
The VHF radio spectrum involves line-of-sight transmission and
reception. This limitation can be overcome by “repeaters,” which pick up
weak signals, amplify them, and retransmit them on a different
frequency. Thus, using a repeater, low-power users (such as mobile
stations) can communicate with one another in situations where direct
user-to-user contact would not be possible. However, repeaters can
interfere with one another unless they are far enough apart or transmit
on sufficiently separated frequencies.
In addition to geographical separation, the “continuous tone-coded
squelch system” (CTCSS), sometimes nicknamed “private line” (PL),
technology can be used to mitigate interference problems. This system
associates to each repeater a separate subaudible tone that is
transmitted by all users who wish to communicate through that repeater.
The repeater responds only to received signals with its specific PL
tone. With this system, two nearby repeaters can share the same
frequency pair (for receive and transmit); so more repeaters (and hence
more users) can be accommodated in a particular area.
For a circular flat area of radius 40 miles radius, determine the
minimum number of repeaters necessary to accommodate 1,000 simultaneous
users. Assume that the spectrum available is 145 to 148 MHz, the
transmitter frequency in a repeater is either 600 kHz above or 600 kHz
below the receiver frequency, and there are 54 different PL tones
available.
How does your solution change if there are 10,000 users?
Discuss the case where there might be defects in line-of-sight propagation caused by mountainous areas.
ICM PROBLEM
PROBLEM C: How environmentally and economically sound are electric vehicles? Is their widespread use feasible and practical?
Click the title below to download a PDF of the 2011 ICM Problem.
Your ICM submission should consist of a 1 page Summary Sheet and a 20 page solution for a total of 21 pages.
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