Motivation
   During the Renaissance it has been a question of honor for mathematicians to challenge or to be challenged in so called intellectual duels, where they proposed each other problems of all kind and style in attempt to prove themselves as the Kings of “The Queen of All Sciences”. Thus, there appeared a tradition of mathematical competitions, in which participated the best of their time. History keeps for us the legend of the algebraic battles of Niccolo Tartaglia and Antonio Maria Fior, as well as, the competition between Lodovico Ferrari and Tartaglia. The problems, carefully chosen and presented to a Notary, have been printed and then distributed among scientists and researchers. Those works, not only brought immortality to those mathematicians, but also had a great influence on the development of science.
   In attempt to continue this noble tradition, in our competition we challenge all teams and classes of secondary school students. Our scope is not searching for great scientific results or young mathematical stars (we’ll be proud to find any). We just want to involve the students in creating and solving problems, to invite them to share the joy and beauty of math thinking, to feel the excitement of discovering new results. We are convinced that the wealth, contained in this part of human knowledge, should belong to all, not only a few chosen.
   The Math Competition aims at developing the capacity to solve problems. It considers the ability of creating mathematical models and posing problems, as well as building up a “taste” for the good and perspective problem.

     First Phase

1. Subscription.
   Each team must have at least 7 members, attending the same Secondary School. The Commission has the right to consider specific applications from teams formed by students from different Secondary Schools. The subscription can be done via Internet at the following address: http://www.dm.unipi.it/~eroe
   The deadline for the subscription is 30 November 2006.
2. Proposal of Problems.
   Each team proposes a math problem (deadline 30.11.2006). There is no need to know the solution of the problem posed.
   The approved problems are published, as anonymous, in the same Internet page, where the subscription is done. The commission has the right to modify the text of the proposed problems, keeping the contained mathematical concepts unchanged.
3. The competition.
   Each team sends the solutions of the solved problems. (Including, eventually, the one posed by them.)
4. Evaluation of the solved problems.
   The commission will assign points to the teams that have sent solutions, considering the number and difficulty of the problems solved.
5. “Democratic” evaluation of the problems.
   All teams vote for the best problem of the proposed. The vote has to be motivated by a brief “evaluation report”. It is not necessary for the considered problem to be solved by the team. The Commission assigns points, based on the “success” of the problem solved by each team throughout the vote.
6. Total Evaluation.
   The Commission assigns additional points to each team that votes for certain problem on the basis of the intelligence and deepness of the critical opinion expressed in the “evaluation report”.

   At the end of the First phase of the competition, the Commission computes a total evaluation, based on the points assigned to the teams during the competition.
   The first 10 teams are considered winners of the First phase and can participate in the competition “Mathematics and comics”, where the Commission assigns points to each team, considering the graphics’ quality and the story of the comics presented and the mathematical quality of the solution proposed. The final classification is based on the points of both First Phase and this competition. The first team wins the opportunity to participate in the Three Days’ Competition in Pisa with costs partially covered by the Commission. The first three teams from the First Phase are also approved to participate in the “Three Days Competition” (The winner of the “Mathematics and comics” is excluded from the classification). The costs of participation of those three teams are not covered by the Commission. If a team refuses to participate, the next classified team takes its place.

     Second Phase: “Three days Math” Competition
   A team is formed by 5-7 participants. One of them is the captain and another one is assigned by the team to bring the solutions to the evaluation Commission. In the final part of the “Three Days Competition” there are around 5 teams.
   The Evaluation Board is composed by Professors from Secondary Schools and Universities.

1. Subscribing.
   The teams are formed by at least 5-7 participants. A responsible professor or teacher from the same school fills the application form (a Word file, that must be signed and sent via mail to the following address):
   
   Sfida di Matematica, Eroemaicantato (V.Georgiev)
   Dipartimento di Matematica, Universita' di Pisa
   Largo Bruno Pontecorvo 5
   56127 Pisa, Italy
   
   or via e-mail to: eroe@dm.unipi.it
   A message confirming the subscription arrives to the professor or teacher in a few days after the application form is sent.
2. First part: The Commission poses 10 specific math problems, in attractive form and modeling interesting and challenging phenomena. Each problem is proposed to the teams and they have 5 minutes to solve it. Then they give their solution to the Evaluation Board. If the Board finds that all solutions of a specific problem are wrong or incomplete, then the Board can give possibility to the audience to give their own answer (solution). If at least one of the solutions is correct, then the Board presents briefly the solution. Then the Board and the teams proceed to the next problem.
3. Second part: The second part consists of a videogame, which introduces a challenging model of navigation. The problem can be proposed a few days before the official competition, so that a strategy for the competition can be planned.

   For more information about the Uknown hero (Eroe Mai Cantato) Competition visit http://www.eroemaicantato.org/ and enter the Math competition section (click "Click per avvicinare l'isola" --> "Click per entrade nella casa del heroe" --> "Click per entrare nelle sfide" --> "Matematica").
   Students from Bulgarian schools who want to participate may also contact:

Iliana Tzvetkova
email address: iliana_tzvetkova@yahoo.com

Oleg Mushkarov
email address: muskarov@math.bas.bg
phone number: (02) 979 38 00