It is even more important that your solutions are correct, complete, and clearly written. You should not expect much credit if your proof refers to a false statement, or even if all your statements are true but you forgot to tell us "why?" It is one of the purposes of the Circle to help you improve your "essay-proof" writing style as well as your logical skills.

Please remember that the Contest is individual. Although we strongly encourage cooperation and help among the participants of the Circle, the Monthly Contest will be one exception to this rule: you may consult your notes, books and other published literature, but you may not ask other people to help you. Other than that, the Contest should offer you the joy of problem solving in an atmosphere close to individual scientific research where the pressure of time limitations is reduced to the minimum. Our intention is to select problems whose solutions will eventually lead you to important pieces of mathematical theory. The more effort you invest into the solutions of your favorite problems, the more you will be able to appreciate the theory behind them. This remains true regardless of whether you manage to complete your own solutions or not. So, you should not give up too easily!

Front: Charlotte Peale (Beginners - 2nd prize, 7th grade), Robert Washbourne (Beginners - 3rd prize, 5th grade), Arav Karighattam (Beginners - 1st prize, 3rd grade), Laura Pierson (Advanced - 1st prize, 6th grade);
Back: Zvezdelina Stankova (BMC Director), Evan Chen (Contest Coordinator, 10th grade), Brian Burns (Advanced - 2nd prize, 10th grade), Daniel Blank (Advanced - 3rd prize, 8th grade)

Each month several winners will be awarded prizes at the Math Circle. At the end of the year, a few grand prizes will be given for highest overall success, and probably for brightest solutions.

 
 
 
Winners of MC8 2012 and Organizers, from left to right:

Zvezdelina Stankova (BMC Director)
Evan O'Dorney (2010-2011 Monthly Contest Coordinator)
Mihir Singhal, grade 5, First Prize in BMC-Beginners Contest
Gregory Young, grade 10, Second Prize in BMC-Advanced Contest
Evan Chen, grade 9, First Prize in BMC-Advanced Contest

All materials here are copyrighted by Berkeley Math Circle; this includes both problems and solutions.

We allow other math circles to use these materials in their own sessions, however, these circles must observe the schedule for the Monthly Contest given below and never discuss these problems before the student solutions will be due in the Berkeley Math Circle. Selling or publishing the materials in this or any other section of the website without the explicit permission of Berkeley Math Circle is prohibited.

LEVELS

• There are two levels of participation. The Beginner Contest comprises four problems numbered 1 through 4 and is primarily for grades 4 through 8. The Advanced Contest comprises five problems numbered 3 through 7 and is primarily for grades 9 through 12. Problems 3 and 4 belong to both contests. Thus the levels are similar to BAMO-8 and BAMO-12, the two levels of the Bay Area Mathematical Olympiad.
• Anyone in grade 8 or younger can participate in the Beginner Contest, and anyone in grade 12 or younger can participate in the Advanced Contest.
• It is possible for a younger student to attempt problems 5, 6, and 7 on the Advanced Contest, and the solutions will be graded and entered into the contest; however, a high school student cannot participate in the Beginner Contest, that is, problems 1 and 2 will not yield a score for a high school student even if correctly solved.

LOGISTICS

• You normally have 3 to 4 weeks to solve the assigned problems; any schedule changes will be announced. Check the BMC schedule for the dates for receiving new MC problems, submitting solutions and receiving awards. Late solutions will not be accepted; if you know in advance that you cannot come to the Circle on the due date, please arrange to submit solutions earlier.
• You may consult any aids - books, notes, etc. - but you may not receive help from other people. Of course, you are on an honor system in this regard.
• Please submit your solutions to different problems on separate pieces of paper, with your name, school, and city, the contest and problem number on each sheet.

WINNER'S HANDICAP

• Depending on funds, there will be serveral awards given for each Monthly Contest to the best papers in each of three age groups.
• In order to encourage everybody to participate and in order to make our competition more fun and challenging for stronger participants, we have enacted a "Winner's handicap" rule.


Anyone who has been awarded a prize in a particular contest will receive a 7-point handicap (a deduction of seven points by default) in every subsequent competition as long as he or she is receiving a prize. If someone manages to win a prize in a contest despite the handicap of 7 points, next time he or she will have a handicap of 14 points, etc. If someone doesn't receive a prize in a contest next time, he or she will compete without handicaps.

GRADING

• The solutions will be graded on a scale of 0 to 7 points, based on completeness, accuracy, and quality of presentation. All four problems on the Beginner Contest and all five problems on the Advanced Contest are equally weighted.
• Extra credit may be given for a substatial generalization, but not frequently
• If a submitted solution is incorrect, the grader will indicate why (if the reason is not presumed to be obvious.
• Because the objective of the contest is to encourage mathematical ingenuity, solutions based on excessively lengthy calculations or solutions which are trivialized by the problem using a computer program may not receive full credit.
• You may refer to well-known results (or less-known results, if you provide a reference), so long as they do not trivialize the problem. For example, if a problem asks for a proof of Fermat's Little Theorem, a solution that says "This is Fermat's Little Theorem; a proof is given in [book, page]" will receive no credit. On the other hand, in a much more difficult problem, it could be appropriate simply to refer to Fermat's Little Theorem when it must be used. When in doubt, include as many proofs as possible.
• The graders' decisions are final and cannot be appealed

These rules are subject to change; any modifications will be thoroughly announced.

Monthly Contest 1

Advanced Contest

First Prize: Laura Pierson (grade 7) with 35 points.
Hillcrest Middle School, BMC Advanced
Second Prize: Brian Shimanuki (grade 11) with 33 points.
Amador Valley High School, BMC Advanced
Third Prize: Vishank Jain-Sharma (grade 11) with 23 points.
Monte Vista High School, BMC Advanced

Beginner Contest

First Prize: Toby Frager (grade 7) with 28 points.
Bancroft Middle School, BMC Intermediate
Second Prize: Arav Karighattam (grade 4) with 25 points.
Homeschool, BMC Advanced
Third Prize: Roma Desai (grade 7) with 22 points.
Ida Price Middle School, BMC Intermediate

Monthly Contest 2

Advanced Contest

First Prize (Klein Bottle): Laura Pierson (grade 7) with 20 points (handicapped from 27).
Hillcrest Middle School, BMC Advanced
Second Prize: Brian Shimanuki (grade 11) with 13 points (handicapped from 20).
Amador Valley High School, BMC Advanced Third Prize: Austin Lim (grade 9) with 7 points.
Benicia High School, BMC Advanced

Beginner Contest

First Prize: Reuben Drogin (grade 8) with 21 points.
Head Royce School, BMC Intermediate
Second Prize: Charlotte Peale (grade 8) with 16 points.
The Crowden School, BMC Intermediate
Third Prize: Ethan Yen (grade 7) with 14 points.
Black Pine Circle School, BMC Intermediate
Third Prize: Emile Givental (grade 8) with 14 points.
Tehiyah Day School, BMC Advanced

Monthly Contest 3
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Monthly Contest 4
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Monthly Contest 5
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Monthly Contest 6
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Monthly Contest 7
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Monthly Contest 8
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