Question 154
a) A championship will have 7 competitors. Each of them will play exactly one game against each of the others. What is the total number of games in the championship?
b) A championship will have $n$ competitors and each of them will play exactly one game against each of the others. Verify that the total number of games is $\frac{n \cdot (n-1)}{2}$.
c) A competitor $A$ is called a master of the championship if every other player either lost to $A$ or lost to someone who lost to $A$. Verify that every championship in which each player plays exactly once against each of the others and in which there are no draws always has a master.
d) João and Maria were in a tournament in which each athlete was supposed to play against each other exactly once. However, Maria had a health problem and left the tournament after playing 10 games, and João had to leave after his first game. At the end of the day, a total of 55 games was counted. Was the game João played against Maria?
b) A championship will have $n$ competitors and each of them will play exactly one game against each of the others. Verify that the total number of games is $\frac{n \cdot (n-1)}{2}$.
c) A competitor $A$ is called a master of the championship if every other player either lost to $A$ or lost to someone who lost to $A$. Verify that every championship in which each player plays exactly once against each of the others and in which there are no draws always has a master.
d) João and Maria were in a tournament in which each athlete was supposed to play against each other exactly once. However, Maria had a health problem and left the tournament after playing 10 games, and João had to leave after his first game. At the end of the day, a total of 55 games was counted. Was the game João played against Maria?