1.1 A courtyard table tennis tournament among 15 players is held according to certain rules. In each round, two players are randomly selected to compete against each other. After the round, the loser receives a black card. The player who receives two black cards is eliminated from the competition. The last remaining player is declared the champion. In table tennis, there are no ties. How many rounds were there in the courtyard tournament if the champion lost exactly once?
Answer: 29

Solution. In each match, there is always exactly one loser. Since 14 players were eliminated, there were a total of $14 \cdot 2+1=29$ losses.