3. At a basketball tournament, 16 teams participate, playing in a double round-robin format, meaning each team plays every other team twice. The top 8 teams advance to the next tournament. The ranking of the teams is determined based on the number of wins, and if multiple teams have the same number of wins, their relative ranking is determined by a draw. How many wins are minimally necessary for a team to secure advancement?
3. We will prove that the answer is 23. First, we will construct an example where 22 wins are not sufficient to advance to the next round. Let's select 9 teams, and let each of these teams win both matches against the remaining 7 teams, while for any two of these 9 teams, in their two matches against each other, they each have exactly one win. Then each of these 9 teams has exactly $2 \cdot 7 + 8 = 22$ wins, and since 8 of them advance, one of these 9 will not. Therefore, at least 23 wins are necessary. These are also sufficient, because otherwise at least 9 teams would have to have at least 23 wins each, which, along with the matches played by the remaining 7 teams, which number 42, would mean that there were at least $23 \cdot 9 + 42 = 249$ matches at the tournament; however, there were $15 \cdot 16 = 240$ matches played at the tournament, a contradiction.