The Mosse Foundation program for education at Mathematical Sciences
Research Institute.

Project of the Mathematical Sciences Research Institute and co-sponsored by the UC Berkeley Mathematics Department and partially supported through the NSF Career Grant to R. Vakil of Stanford University.

Bay Area Mathematical Olympiad 2005

The BAMO 2005 Exam took place on Tuesday, February 22, 2005 at participating schools. The awards ceremony took place on Sunday, March 6, 2005 at the University of San Francisco.

Problems from the 2005 BAMO exam can be found here (PS | PDF). Solutions to the 2005 BAMO exam can be found here (PS|PDF). Results can be found here.

The annual BAMO contest was an annual exam given to students at participating high schools and middle schools, most of whom were in the San Francisco Bay Area. The exams were mailed out to the schools, proctored locally, then returned to be graded by a group of math circle instructors and educators.

The following weekend, there was an awards ceremony, with prizes for individuals and schools, lunch for everybody, and a math talk entitled "Ramsey Theory: Amongst enough chaos, can we find order?" by special guest Melanie Woods, from Princeton. The abstract of her talk is below:

ABSTRACT: Suppose we are given a plane with all its lattice points colored either red or blue.
Can we always find a rectangle with all four vertices colored the same color? If that's too easy,
then we can try to find a square with all of its vertices the same color. All of a sudden, the
problem is much harder and leads us to a more general question. Given enough "stuff," colored
in some manner that we have no control over, when can we find a monochromatic version of
some structure? We'll discuss versions of this question ranging from concrete to abstract,
and we'll even see what this says about winning strategies for higher dimensional tic-tac-toe.

The event has been hosted each year by a different academic institution in the Bay Area: UC Berkeley in 1999, University of San Francisco in 2000, Mills College in 2001, San Jose State University in 2002, Stanford University in 2003, UC Berkeley in 2004, and now the University of San Francisco in 2005. The awards ceremony has become an annual focal point for the Bay Area middle and high school activities, where 180-200 students, teachers and parents gather for an exciting day of Mathematics. The event has been made even more worthwhile by the staggering sequence of famous lecturers and their fabulous talks:

1. Alan Weinstein (University of California at Berkeley), "The Geometry of Random Expectation", 1999.
2. Persi Diaconis (Stanford University), "Card Tricks and the Mathematics of Magic", 2000.
3. Ron Graham (University of California at San Diego), "Mathematics in the 21st Century: Problems and Prospects", 2001.
4. Joseph Gallian (University of Minessota at Duluth), "Breaking Driver's Licence Codes", 2002.
5. Ravi Vakil (Stanford University), "Why is the Golden Mean Everywhere?" 2003.
6. Joe Buhler (Center for Communications Research and Reed College), "Juggling Permutations," 2004.
7. Melanie Woods (Princeton University) "Ramsey Theory: Amongst enough chaos, can we find order?" 2005.

The 20 individual BAMO prizes and 12 honorable mentions were awarded in 3 age groups: 11-12th grades, 9-10th grades, and 8th grade and below. The 3 age group categories gave the opportunity for younger participants with less mathematical experience to be acknowledged for their bold and creative participation in the Olympiad. This year there was one grand prize awarded for the highest overall BAMO score, which was 29/35. In the 11th-12th grade category, there was a 3-way tie for first place, 2-way tie for 4th place, and 2-way tie for 6th place plus 5 honorable mentions. In the 9th-10th grade category, there was a 3-way tie for first place, 2-way tie for 4th place, and 2-way tie for 6th place plus 5 honorable mentions. In the 8th grade and below category, there was a 1st place winner and a 4-way tie for second place plus 2 honorable mentions. Every prize winner and honorable mention student received a specially designed BAMO 2005 t-shirt with problem 5 on the back.

The difficulty of the BAMO problems ranged from very easy and accessible to middle school students problem 1 to a die-hard problem 5, usually solved by only a handful of students, if any. This year problem 5 was a 3D solid geometry problem which was expectedly very hard, and the only nonzero scores were 5, 4, and 1. The score of 5 was held by a female participant.

Some of the prizes this year included a camcorder, portable DVD player, Apple iPods/iPod Minis/iShuffles, digital cameras, Xavix Virtual Reality System and VR baseball game, MAA published math books, gift certificates for AMC theaters, Borders, and Hardrock Café, as well as 4 ping pong tables. In total, the prizes amounted to about $6000!

BAMO has been held each year in February, with the first one having taken place in 1999 (one year after the founding of Berkeley Math Circle). The average participation is 250 students from approximately 45 schools.