The Mandelbrot Competition

Administration....Forms of Answers....Scoring/Prizes
[Mandelbrot Team Play Rules]

The rules below are a summary of the guidelines appearing in the welcome packet and on the Frequently Answered Questions pages. Coordinators should be familiar with all of these rules prior to the first round, particularly those concerning administration and scoring. Please pardon the terse exposition. After all, this is a page of nothing but rules!


  • Any accredited high school may register for the Mandelbrot Competition.
  • Students under the age of twenty who are not affiliated with a participating high school, such as home-schooled students, may also enroll in the contest provided that there are at least three committed students sponsored by an adult who agrees to act as the coordinator. Arrangements may be made by contacting Greater Testing Concepts.
  • Greater Testing Concepts reserves the right to disqualify a school and refund the registration fee at any point during the course of the competition.
  • Schools selecting the mail delivery option will be sent a welcome packet containing instructions, forms, contest originals, and ribbons by early October. Coordinators opting for electronic delivery will download these materials from the web site, except for the ribbons. All coordinators will be assigned a four-letter school code and an account at the web site through which they may update school information and manage individual names and scores.


Scheduling / Levels / Regions

  • The Mandelbrot Competition takes place over the course of five rounds spread throughout the school year. (The dates for each round are displayed on the Information page.) Schools that are unable to participate during the official week may reschedule the contest for the week immediately before the official contest window. Schools which have conflicts with both of these weeks must contact Greater Testing Concepts before making alternate arrangements.
  • The Mandelbrot Competition is offered at two levels: the National Level for advanced students and the Regional Level for less experienced problem solvers. Schools may register in either or both levels. However, schools participating for the first time should enroll in the regional level only.
  • Since the regional and national tests have several questions in common, a student from a school enrolled at both levels may take only one set of tests. For the same reason, the tests for each level should be given simultaneously.
  • There are currently five geographic areas which define the regional leagues, described on a FAQ page.



  • As many students may take the Mandelbrot Competition as the coordinator desires. Copies of the test original should be made no sooner than two school days before the contest is administered.
  • Forty minutes are allowed for the Mandelbrot Competition. No external aids such as calculators, notes, textbooks, graph paper, rulers, etc. are allowed. Students must work independently on the test. Dictionaries are not allowed, even for international students or schools competing from other countries.
  • At the conclusion of the contest period the proctor should collect all test papers and scrap work and retain them until the weekend following the official contest week. On Thursday an answer key with solutions will become available at the web site for coordinators upon login to their Mandelbrot account. The coordinator may then score papers, enter scores at the web site, and return tests and solution to students the following week.
  • Each round consists of seven short-answer questions, ordered from easier to more difficult. The first two questions are worth 1 point each, the next three are worth 2 points each, and the last two are worth 3 points, for a maximum score of 14 points.
  • No partial credit is awarded on the Mandelbrot Competition. Any answers that are clearly equivalent to the answer provided may be awarded full credit. The proctor has discretion in deciding whether an answer is acceptable; if there is a question of equivalency the coordinator should contact Greater Testing Concepts for a ruling.
  • If a coordinator wishes to dispute an answer or feels that a question was ambiguous, the coordinator should send an explanation of the disagreement to Greater Testing Concepts as soon as possible. Students must forward disputes through their school coordinators.


Form of Answers

  • In general, our philosophy is to award credit on the Mandelbrot Competition whenever a student successfully solves a problem. Therefore if a student writes an answer which is clearly equivalent to the answer in the key, such as 69/60 instead of 23/20 or 1/sqrt(2) instead of sqrt(2)/2, then credit should be awarded. However, please encourage your students to write their answers in simplest form, as outlined below, to avoid any ambiguity or gray areas.
  • Please do not hesitate to contact Greater Testing Concepts with inquiries as to how to score a student's response. The most difficult judgments to make occur when a student gives an answer which is numerically equal to the answer in the key, but which requires more than a trivial simplification to reduce to the correct solution. Coaches should forward these scoring questions via the Dialogue page rather than trying to pass judgments themselves so that we can announce all appeals to ensure that the contest is scored as consistently as possible. (For example, an answer of instead of 2 should not receive credit.)
  • Fractions should be written in lowest terms. In general we recommend that students write fractions rather than decimals when either is an option. Improper fractions are fine, so both 5/3 and 1 2/3 are acceptable.
  • Simplify square roots so that no perfect squares appear under the radical sign. Also, square roots should not appear in the denominators of fractions.
  • Probabilities should be reported as a real number between 0 and 1 inclusive, usually as a fraction. Do not write percents or odds when answering a probability question.
  • Units are not required, but must be correct if given. In other words, if a question asks for the length of segment AB in cm and the correct answer is 2cm, then responses of 2, 2cm, or 20 mm would all be correct, but 20 alone would be incorrect.
  • Angles should be written in the same units given in the question, normally degrees.
  • Special directions in a particular problem take precedence over these general guidelines.


Scoring and Prizes

  • A student's score for the year is the sum of their individual scores from all five rounds.
  • The highest scoring students within each league (at the national level as well as within each region) will be declared Mandelbrot winners and given a snazzy prize which will vary from year to year. Past prizes have included special Mandelbrot playing cards, cool Mandelbrot Frisbees, and limited edition Mandelbrot T-shirts. At least ten students from each regional league and twenty students at the national level will be honored; the exact number depends on whether or not there are ties.
  • School awards—four ribbons for high scorers at each level—will be included with the welcome packet for every school opting for mail delivery of materials.
  • A school's score for a given round is the sum of the four highest individual scores on that round. A school's score for the year is the sum of its scores for the five rounds.
  • The top three distinct schools within each region along with the top five distinct schools at the national level will receive a large engraved commemorative plaque. (In other words, at most one plaque will be awarded per school per league.)

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