3. At the international StarCraft championship, 100 participants gathered. The game is played in a knockout format, meaning in each match, two players compete, the loser is eliminated from the tournament, and the winner remains. Find the maximum possible number of participants who won exactly two games?
Answer: 49

Solution: Each participant (except the winner) lost one game to someone. There are 99 such participants, so no more than 49 participants could have won 2 games (someone must lose 2 games to them).

We will show that there could be 49. Let's say №3 won against №1 and №2, №5 - against №3 and №4, ... №99 - against №97 and №98, and №100 won against №99. Then all participants with odd numbers (except the first) won exactly 2 games.