The Berkeley Math Circle

Contest Rules


  • 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.


  • 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.


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.

  • Depending on funds, there will be several 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.

  • A winner's handicap from the Beginner contest does not apply to the Advanced contest, but a winner’s handicap from the Advanced contest applies to both contests.


  • 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 substantial 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.