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Below I attach some articles of the regulations of the national mathematics finals held in Cesenatico (IT) in 2023. In accordance with these regulations, the program was created.

Here is the English translation of the "Regolamento per le gare a squadre" (Rules for team competitions) held in Cesenatico, 5-6 May 2023:

5. The competition consists of solving problems assigned during the competition time (90 minutes for a semi-final, 120 minutes for a final).

6. At the start of the competition, each problem is worth 20 points; up to 20 minutes from the end of the competition, the value of each problem increases (a) by 1 point per minute, until the problem receives correct answers from n teams; (b) by 2 points for a wrong answer given by each team to the problem (any other wrong answers given by the same team do not increase the value of the problem). Therefore, if n > 1, the first n - 1 teams that solve a problem correctly immediately receive the points of the value of that problem; the value of the problem continues to increase and the score of those teams grows accordingly. If the problem is a joker for a team, all these points are doubled. 20 minutes from the end of the competition, the values of all problems stop increasing. A scoreboard shows the instantaneous value of the scores.

7. The slip is brought by the deliverer to the delivery table. The jury evaluates the correctness of the answer as soon as possible; the deliverer obtains the information on the correctness of the answer by looking at the status of the answers panel. If the answer is wrong, the team loses 10 points, but can go back to thinking about the same problem and then subsequently provide another answer. If the answer is correct, the team earns a number of points equal to the value of the problem plus a bonus, which depends on how many teams have already provided the correct answer to that problem. For each problem, a bonus of: 20 points is awarded to the team that solves it first, 15 points to the second, 10 points to the third, 5 points to the fourth, 3 points to the fifth. Obviously, any penalty points previously accrued on the same problem remain. The instantaneous values of the problem scores listed on the scoreboard do not include the possible bonus available.

8. If a team delivers a correct answer to the same problem twice, it takes the score only once. If, on the other hand, it delivers wrong answers to the same problem several times, it incurs the penalty of 10 points several times. The penalty is also assigned if a team delivers a wrong answer to a problem to which it has already provided the correct answer.

9. During the first 10 minutes of the competition, each team must choose its "joker problem". The decision must be communicated (within 10 minutes) by the deliverer to the delivery table on a special slip. Every score obtained by the team on that problem from that moment on (problem score, any bonuses or penalties) is multiplied by two. Each team must have a "joker problem": after 10 minutes without communications from the deliverer, the first problem on the list is officially assigned.

10. At the start of the competition, each team starts with a score of ten times the number of problems.

11. A bonus is also awarded to the first five teams that solve all the problems correctly, regardless of the wrong answers provided along the way. For this, 50 points will be awarded to the first team, 30 to the second, then 20 to the third, 15 to the fourth, 10 to the fifth.

12. At the end of the competition, the ranking is compiled based on the scores accumulated up to that point. In case of a tie between two or more teams, the one that has scored the most points (including bonuses and penalties) in its "joker problem" prevails. In case of further parity, the team that obtained the highest score for a correct answer prevails; if parity still exists, the second highest score is looked at, and so on.

13. Given that, despite all the attention and checks that we put into the preparation of the problems and the management of the competitions, there is always a small probability of material errors in the calculation of the scores - due to, for example, a wrong response communicated to the tables, an error in the text or an error in the calculation of an official answer -, some of the procedures provided for in cases of this kind are listed below. (a) No adjustment is provided for reading errors of the answer sheets when these are actually ambiguous. The teams are responsible for ensuring that the numbers written on the slips are clear and unambiguously readable. (b) In case of material errors in the calculation of the scores (due for example to an incorrect calculation of the official answer), the ranking is reconstructed as it would have been with the correct answer and based on the answers actually delivered, with one exception: the penalty for the delivery of a wrong answer is canceled if previously the same team had delivered a correct answer to the same problem which, at the time of this new delivery, is erroneously evaluated as wrong. (c) In case of material errors in the assignment of the score, the organizers will do their best to reconstruct the exact scores as soon as possible based on the deliveries made and the data available to them, correcting the rankings in progress or, if necessary, even after the competition. We point out.

Source: regolamento_fgs23.pdf