• The tournament will consist of five rounds.
• In each round, there will be four teams per room in each of four rooms.
• The 16 teams will move among the four rooms in the following rotation. (Here team 1 is the highest seeded team present at the start of the tournament, team 2 the second highest seeded team present at the start of the tournament, and so on, the seedings being determined by the team score on the first round written Comprehensive test.)

 Round 5

• In this rotation, each team will be in the same room as each other team exactly once and, to maintain suspense for the entire tournament, the top four seeds will be in the same room only in the final round.
• In each round, each team will consist of four members. You may use as your team any four students you wish. They need not be your highest scoring students from the first round. They need not have competed in the first round at all. You may use different students in different rounds if you wish. Prior to each round, you will deliver to the room monitor a list of your four competitors, numbered 1,2,3,4. Your #1 will cipher two individual questions against the three opposing #1 students, then the #2’s will take two questions, and so on. The #1’s will receive two geometry questions. The #2’s will receive two algebra questions on material through Algebra II with Trigonometry. The #3’s and #4’s will each receive two comprehensive questions, which may be on any topic. (We repeat that you may use any students you wish in any position. However, you might prefer to use bright sophomores or juniors in the #1 and #2 positions and to use more experienced students in the #3 and #4 positions.) Individual questions will have a time limit of two minutes. After the eight individual questions, your entire team will cipher two questions against the three opposing teams, with consultation among team members allowed. The time limit on team questions will be three minutes. The team questions will complete a round of ten questions.
• In each round and in each room, each team in the room will be playing each of the other teams in the room in a one-on-one match. That is, there will be 6 ("4 choose 2") matches occurring simultaneously in each room. Each one-on-one match will be scored as if the two other teams in the room were not present.
• As a result, each team will play three other teams in each of the five rounds, and in the end will have played each of the other 15 teams exactly once.
• For each question, the scoring will be as it has always been: 2 points for the first correct answer, 1 point for a subsequent correct answer, and 0 points for no answer or an incorrect answer. But in each round and in each room, this scoring system will be applied separately to each of the 6 matches.
• So for example, let us suppose that in Round 4 / Room 1, team 7 gives a correct answer, then team 12 gives a correct answer, then team 1 gives an incorrect answer, and finally team 14 gives a correct answer. Then the question will be scored as follows for each match: #1 vs. #7: 0 to 2 points, #1 vs. # 12: 0 to 2 points, #1 vs. #14: 0 to 2 points, #7 vs. #12: 2 to 1 points, #7 vs. #14: 2 to 1 points, #12 vs. #14: 2 to 1 points. The final score of each of the six matches taking place in a given round and a given room will be the sum of the scores for each of the ten questions.
• The scoring of the tournament will be as in a standard round robin tournament. When team A beats team B, team A will be awarded 1 point and team B will be awarded 0 points. If team A ties with team B in a match, the tie will not be broken, and each team will be awarded 1 point.
• At the end of the tournament, each team will have scored from 0 to 15 points. Ties will be broken first on the basis of head-to-head matches. That is, if team A and team B have each scored 12 points, but team B won its match with team A, then team B will finish ahead of team A. A tie for first place which remains unbroken after this consideration will be broken by a mini-match consisting of five questions (followed, if necessary, by a "sudden-death" match consisting of more team questions.) Ties for places other than first place will be broken by the original seedings.
• If there are fewer than 16 teams, which is usually the case, the same rotation will usually be played. Teams not actually present will be "ghost teams", against which any real team will win. (This is fair since each real team will play each ghost team exactly once.) A team which leaves early (though we strongly discourage this) will effectively become a ghost team after it leaves. Late arrivals could join the tournament in progress by taking the place of the highest numbered ghost team. (If we are certain that a maximum of 9 teams will compete in a given division, we may use a similar rotation designed for 9 or fewer teams and using only three rooms. In the unlikely event that there are only 6 teams, we will use a standard round-robin rotation for 6 teams.)

• Fairness: Because every team plays every other team exactly once, the tournament is essentially the same for every team. It is as close to a true round robin tournament as we can possibly arrange. Also, almost every team plays almost every round. The only times when a team would have to sit out a round would be in the cases where there are 9 or 13 teams actually present, in which case the lowest seeded team present would have no actual teams to play in the last round. In the unlikely even that only 7 teams were present, each of the top four seeded teams would sit out one round. In the very unlikely event that only 6 teams were present, an ordinary round robin tournament could and would be played, so of course every team would play every round.
• Timeliness and Clarity: The schedule for where each team needs to be in each round will be made out in advance of the tournament. We will write it down and give a copy to each sponsor as he or she arrives on Saturday morning. Everyone will know where he or she should be at all times and there will be no waiting between rounds for pairings to be made! (The tournament begins early in the morning and finishes at about 12:00 noon, so efficiency is very important.)