Logistical requirements Facilities, Equipment, and Staff Consider a field containing n teams. All games are played by pairs of teams. Therefore, the greatest number of games that may occur at a given time when n is even is n/2. When n is odd, meanwhile, an odd number of teams cannot play a given game; rounds in which a team does not play are called the bye rounds of a given team. The maximum number of games that can occur at once when n is odd is (n-1)/2. Every game requires one room in which to hold it, one set of questions, one buzzer, one clock in timed formats, at least one scoresheet, one moderator, and, if possible, one scorekeeper. Therefore, when preparing for a round robin of n teams, one should first guarantee for the length of the round robin n/2 rooms, question sets, buzzers, clocks when necessary, scoresheets, moderators, and scorekeepers; (n-1)/2 of each of these items is necessary when n is odd. Throughout this tournament, it is assumed that the above is available throughout the round robin. For exceptions, see the section Constrained Cases. Time & number of rounds Generally, the time a round robin requires to be played is equal to the sum of the lengths of all the rounds, plus any transition time between rounds. Where T is the total time consumed, t is the expected length of a round, r is the number of rounds, i the number of iterations, and m is the transition time, T = ir(t + m). Allot T time on your schedule. It is standard practice for m to be considered a part of t. Draft your schedule, then, in ir increments of t. Consider again a field containing n teams. In one iteration, a given team will play every team except itself only once; therefore, each team will play n-1 games. This is common to all round robins. There are now four cases to consider, based on two variables: 1. there are an odd number of teams in the field, and the questions for each round are submitted by each team; 2. there are an odd number of teams in the field, and each team is blind to all the questions to be used; 3. there is an even number of teams in the field, and the questions for each round are submitted by most or all teams; 4. there is an even number of teams in the field, and all teams are blind to all questions. Case 1 is the most frequent situation for invitational tournaments. Each team cannot play on its own questions. Meanwhile, all matches occur between pairs of teams; therefore, in any round, an odd number of teams must not be playing; assuming a sufficient number of rooms, only one team cannot play in a given round. These two constraints correspond neatly; therefore, the questions a team submits should be played on in the round that that team does not play. Since a team (in general) submits only one round of questions, has only one bye round, and plays each opponent once, we find that one iteration of a submission round robin containing n teams requires n rounds, where n is odd. Case 2 is identical to case 1, except that teams do not submit questions. However, the same constraint requiring that matches be played only between pairs of teams persists. Therefore, each team still must receive a bye round, even though its questions are not being used. >From examination of these two cases, we find that when n is odd, a round robin for a field of n teams requires n rounds.
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