Maths Combat is a competition between two teams in solving mathematical problems. First of all, the teams are presented with the problems and given a certain time limit to solve them.
While solving the problems, the team may use any literature, but is not permitted to talk about the solution to these problems with anyone except with the members of the jury. At the end of the allotted time, the actual battle begins, when the teams present the solutions of the problems in accordance with the given rules.
One of the teams presents the solution, the other acts as an opponent and looks for mistakes (defects) in the presentation. The jury rates the speeches of the speaker (the team member presenting the solution) and the opponent (the team member opposing the speaker) by allocating points to each of them in accordance with the rules.
If the teams have neither solved any problems by the end of the given time nor found any mistakes while discussing the proposed solution, the jury of the battle can take some of the points available in the round (or even all of them).
The winner of the battle is the team that gets the most points in total.
If, at the end of battle, the results of the teams do not differ by more than three points, the battle is considered to have ended in a draw. If, for some reason, the battle cannot end in a draw, the jury is to declare this to the teams before the battle and announce the procedure for determining the winner.
The General Scheme of the Battle
The battle consists of several rounds.
At the beginning of each round (if there is no rejection of the challenge – see para. “The End of the Battle”), one of the teams challenges the other on one of the problems, the solution of which has not yet been presented (for example: “We challenge the opposing team on problem number 8”). Then, the challenged team announces whether it accepts the challenge, i.e. whether it agrees to present the solution to this problem (it is given no more than one minute to make a decision on the challenge). If a team accepts the challenge, it nominates a ‘speaker’, who explains the solution. The team that made the challenge nominates an ‘opponent’, whose duty is to look for errors in the presented solution. If the challenge is not accepted, then the team that made it is obliged to nominate a speaker, and the team that rejected the challenge has to nominate an opponent. In this way, one can consider that the reasonableness of the challenge is being assessed.
The Captain’s Competition
The ‘captain’s competition’ is held at the beginning of the battle.
The team that wins the captain’s competition determines which team makes a challenge first.
The captains are given a problem. The first captain to inform the jury that she/he knows the answer to the problem gets the right to explain it. If he/she presents the correct solution, he/she wins, but if it is incorrect – his rival wins. This is what is meant by “the correct solution”: simply the correct answer, the answer with an explanation, and so on – the jury specifies the nature of the correct answer before the competition of the captains begins.
The jury assigns a specific period of time for the solution of the problem for the captain’s competition. If, during this time, none of the captains express their desire to answer, the jury may replace the problem or determine the winner by draw. Instead of the problem the jury can offer to the captains to play in any game. There are other methods of carrying out the captain’s competition.
The jury determines the way the captain’s competition will be held in advance and informs the teams before the beginning of the battle.
Each team has the right to nominate any member of their team for the captain’s contest.
The Progress of the Round
The speaker has the right to:
- write/draw any necessary information on the whiteboard before the presentation;
- not answer any questions raised by the opponent before the beginning of the discussion;
- ask the opponent to clarify his question (in particular, the speaker may propose his own version of the question: “Do I understand correctly, that you asked me about something and something?”);
- refuse to answer the question, by saying that
- he has no answer to this question;
- he has already answered this question (explaining when and how);
- the question is incorrect or beyond the scope of scientific discussion for the stated problem. In case the opponent disagrees with the basis of 2) and 3) the jury arbitrates the dispute.
The speaker is not obliged to:
- explain how he/she worked out the solution if he/she can prove that it is correct and complete;
- compare his way of solving the problem with other possible methods, including in terms of brevity, beauty and aptitude for solving other problems.*
Participation of the jury in the discussion
Speakers and the team
The correctness of the challenge
If the challenge is accepted by one team, then the question of its correctness is not considered. If the challenge is not accepted, then there are two possibilities:
- if the team that made the challenge also refuses to answer, then the challenge is automatically deemed invalid;
- if the team that made the challenge nominates the speaker, then the correctness of the challenge depends on the consequent progression of the round.
The challenge is deemed incorrect if the opponent manages to prove that the problem is not solved. In the case of the opponent declaring the problem solved, the challenge is “automatically” accepted as correct!
Number of Appearances at the Blackboard
The Challenge Procedure. End of the Battle
Each problem is worth 12 points, which are distributed between the speaker, the opponent and the jury by the end of the round. If the speaker presents a correct and complete solution, she/he gets all 12 points.
If the opponent was able to find significant errors in the solution, the jury decides whether the opponent was able to prove that the speaker does not solve the problem. If the opponent fails to do so, she/he can nevertheless get the points for opposing, depending on the gravity of the defects of the presentation and how the speaker (or an opponent if there was a partial change of roles) managed to fix them. Generally, the opponent receives half of the “cost” of the “holes” that were not “patched up” by the speaker in the solution (the principle of “half”). However, if the speaker was able to present a complete solution only after considerable errors in the solution are found by the opponent and/or the jury (“mud” in solution), then the jury can take away up to two points from the speaker and transfer it to the opponent, or leave it for themselves. If there was a change of roles, the former opponent gets extra points for proving the statements that were formulated prior, as does the former speaker – for her/his opposition (the “cost” of the concerned statements is defined by the jury, and the distribution of the points happens in the same way, as when opposing a complete solution – taking into account the principle of “half” and “dirt” in the debates). The remaining points are distributed between the speaker and the jury, and the round ends. If the opponent fails to prove that the speaker has no solution, she/he gets points for opposing it (taking into account the principle of “half”). If the challenge was accepted, the opponent gains the opportunity to present his solution (see para. “Role reversal”).
If this is accompanied by a complete or partial change of roles, then the scoring process proceeds according to the method described above.
If the errors or gaps in the report are pointed out by the speaker himself and are not taken care of by his team, the opponent receives points for them, as if she/he had found these drawbacks himself.
If the captain of the challenging team immediately admits that his team does not have a solution after his challenge had been refused by the other team, the opponent’s team receives 6 points for opposing (which in this case consists of a single sentence: “You have no solution”), and the challenge is accepted as incorrect. In this case, the speaker and the opponent are not nominated and the appearances at the whiteboard are not counted.
During the battle, only the captain can speak to the jury and contestants on behalf of his/her team: to challenge the other team, to refuse or accept a challenge, to request a break, and so on. He/she has the right to stop the presentation or the opposition of a representative of his team at any time. If the captain is at the whiteboard, she/he nominates a deputy, who performs the duties of the captain at this time. The names of the captain and the deputy are reported to the jury before the beginning of the battle.
The primary responsibility of the captain during the solving of the problems is to coordinate the actions of the team members to solve as many problems as possible. To do so, the captain distributes the problems amongst the team members, taking their wishes into account and ensuring that every problem is being solved by someone. The captain also organises the checking of solutions, to make sure they are correct. The captain determines who the speaker and the opponent in the upcoming battle will be and determines the team tactics.
The captains of the teams have the right to ask the jury to provide 5-10 minutes breaks during the battle (approximately every half hour). The break may be provided only between rounds. The team, which is to make a challenge, does so in writing (without an announcement) immediately before the break and hands it to the jury, which announces the challenge immediately after the break.
The jury is the supreme interpreter of the rules of the battle. In situations, which are not covered by the rules, it shall decide at its own discretion. The teams are bound by the jury’s decisions.
While the teams are solving the problems, every significant clarification of the problem that was given by the jury to one of the teams should be reported as soon as possible to all of the other teams.
The jury may withdraw the question of the opponent (for example, if it has no merit), or stop the presentation or the opposition if they are taking too long. If the jury cannot gain an understanding of the solution quickly, it may, with the approval of both captains, allocate its representative, who will continue to discuss the problem in cooperation with the speaker and the opponent in another room. During this time, the battle continues with other problems, and the points for these problems are awarded later.
The jury writes the battle protocol on the whiteboard. If one of the teams does not agree with the decision made by the jury regarding the problem, it has the right to immediately demand a break for a few minutes to discuss the situation with the participation of the chairman of the jury. After the beginning of the next round, the score of the previous round cannot be changed.
The jury keeps order. It can penalise the team for noisiness, inappropriate behaviour, or communication with their representative who is located at the whiteboard.
The jury is obliged to give reasons for all of its decisions that do not follow directly from the rules of the battle.