(Originais Teachy 2024) - Question Hard of Physical Education

During an intercollegiate championship, a group of 3rd-year high school students decides to organize an 'Ultimate Frisbee' competition in which teams are formed in such a way that each team has an equal number of male and female players to promote gender equity and inclusion in the sport. As the student Pedro noticed that, in general, there are more male students than female students in the championship, he proposed a strategy to organize the teams in a way that, considering the total number of players and the gender ratio, all teams have the highest possible number of male and female players, maintaining equity. Assuming there are 72 students registered in the championship and the ratio of male to female players is 3 to 2, what would be the gender composition of each team, and how many teams can be formed following Pedro's proposal? Additionally, Pedro raised the issue that in previous championships, matches often started with players incorrectly positioned on the field, due to an insufficient understanding of the positioning rules. Based on the rules of Ultimate Frisbee, which require each team to start with seven players on the field, and that alternating teams must start in opposite positions, sketch a diagram representing the initial arrangement of male and female players on one of the teams, and explain how knowledge of these rules can help avoid errors in team formation.