Ciphering

A school may enter as many students into ciphering as it wishes, but no students from the same school may sit next to each other. After three rounds, the top four teams will participate in the math bowl competition.

Each individual is given a booklet with one problem per page. In addition to the problem, each page will have space for scratch work, a block for answers, and a space for the individual's code. Improper code or lack of code will disqualify an answer.

All answers must be in exact, simplified form unless otherwise requested. All fractions must be reduced and all radicals must be simplified. Remember that 1 / √3 is acceptable, but 6 / √3 is not because it can be reduced to 2v3. Units are not necessary unless specifically requested, but if units are included, they must be correct.

Two minutes are allotted for each question. When students answer the question, they will raise their sheets above their heads for runners to collect. Four points are awarded for answering the question correctly within one minute, while two are awarded for answering correctly within two minutes.

An individual will receive an overall score, while the team totals will be used to determine who advances to math bowl. Each school's cipherers will be ranked by score and set in teams of four from the top downward; the four teams with the highest totals will compete in math bowl.

The individual from each division with the highest total score after three rounds will receive a trophy, but no points will be added to sweepstakes.

Math Bowl

Math bowl is the semi-final and final rounds of ciphering. Teams will be seeded into a four-team bracket by total ciphering points after the three rounds of ciphering are completed. In the semi-finals, the highest and lowest scoring teams will be matched, and the second and third scoring teams will be matched. In the finals, the winners of these two will be matched for first and second place and the non-winners will be matched for third and fourth place.

Each math bowl match consists of 20 questions: 10 one-minute tossups, and 10 two-minute bonuses. Each question is worth 10 points. Any team member may answer a tossup question by raising his/her hand and being recognized by a spotter but team members will not be allowed to confer; if he/she answers correctly, the entire team may confer on a bonus question. Only captains may answer bonus questions. If a tossup is answered incorrectly, the other team has either the remaining time or 10 seconds (whichever is longer) to answer. If a bonus question is answered incorrectly, the other team may not answer. A 10-second warning will be given for both tossup and bonus questions.

See the rules for simplification in the ciphering description above.

Gemini

There will be three rounds of Gemini questions from which the four highest-scoring teams will move on to a semi-finals/finals round. Each school may enter up to 3 teams per division.

Gemini will be a two-person, cooperative event consisting of a series of timed problems similar to the ciphering format. Each two-member team will work together on questions of varied type and time limit. The packet of questions will contain 3 problems per page, each scored separately. The questions will not be as subject-specific as ciphering, but will incorporate a “potpourri” of mathematics with an emphasis on logical thinking and problem solving. Ciphering simplification rules apply.

A team of members in different divisions will compete at the level of the most advanced student. There are no calculus-based questions in Gemini.

Hustle

Hustle is a team event in which each team attempts to outscore its opponents by quickly solving more problems. Each team will consist of 4 members. A team can have no more than one Mu Division student and must have at least one Theta Division student. No school may enter more than two Hustle teams.

Teams receive 125 problems each round, grouped into sets of 25. These will be distributed in packets and must remain untouched until the moderator begins the round. A round will consist of several ten-minute hustles. The moderator will announce the beginning of each hustle, give five, two, and one-minute warnings and simultaneously call the end of the hustle and the beginning of the next.

By the end of each hustle, each team will submit answered items as directed by the moderator. A team may submit no more than five items of each color in any one hustle. Up to 5 items of each color must be paper-clipped together and held up before the end of the hustle to be collected by a moderator.

Each correctly answered item submitted in hustle one will score 6 points, in hustle two 5 points, etc. If a team miscounts and submits more than 5 items of one color, the incorrect items will be tallied first and any above the limit will be thrown out, thus scoring the smaller number of points.

The four teams with the highest cumulative scores after the preliminary rounds will enter the finals, which will consist of two shortened rounds. The final ranking of these four teams will be determined by the total scores of the two final rounds, with the preliminary round scores considered only if necessary to break a tie.

Ciphering simplification rules will be followed unless otherwise specified.

Descartes

This is an individual competition in which two (or three) opponents, facing each other, compete with the objective of scoring the most points. Each school may enter up to three students per division.

At the beginning of each round, the moderator gives each player an envelope with 50 points worth of cards. Each card has a question on one side with a point value of 1, 2, 3, 5, or 10 according to estimated difficulty and the answer on the other side. Each round consists of three periods. A period consists of opponents playing each other twice. At the end of a period, players will move as instructed and the next period will begin with players having new opponents.

Each period is divided into two parts, each consisting of three phases. The first phase is the bidding time. The bidder chooses the combination of cards that he wants to play for a total of 10 points, but a limit of five cards. Each player removes that combination of cards from his envelope. The bidder may have to compromise according to what cards are available to his opponents as the game progresses. Each player places the chosen combination of cards, question side up, on the table in front of his opponent. The second phase of play is the playing time. During this time each player works the questions presented to him. A player must not pick up any card during the playing time. When a player finishes working a question, he covers that card with his answer sheet. A player may work problems in any order and may leave one temporarily to work another. A player may not consult any person except a moderator. When time is called, all pencils must be placed on the table. The third phase is the scoringtime. The cards are turned over with their respective answer sheets so both players can see all cards answer-side-up and solutions to facilitate quick agreement. If an answer is correct, the player who solved it keeps the card. If the answer is incorrect, his opponent keeps the card. If there is a point of confusion, a moderator will come to the table in response to a raised hand. A moderator may give a 10-point penalty to a player for withholding or mutilating cards. Players then put all the cards they now have into the envelope and part two of the period begins. Part two of the period is a repeat of part one with the exception that the opponent of the player who bid in part one will bid. Repeat phases 1-3. At the conclusion of the period, each player counts the points on his cards and records the total. He then exchanges cards with his opponent to verify the total.

Second period begins with the players keeping the cards that they have from the first period and changing seats to compete against another opponent. Follow the instructions for first period. Once second period is complete, third period begins.

Semifinals and Finals: The top four scorers at the end of all three rounds proceed to the final rounds. The first and fourth place scorers will be matched and the second and third place scorers will be matched in the semifinals. Then the winners of the semifinals will be matched for first and second place in the finals and the non-winners of the semifinals will be matched for third and fourth place in the finals.