Question

There are 64 volleyball teams in the state competition. In the first round of play, each team plays one other team, so 32 games will be played in the single elimination tournament. The winners from these games play each other in a second round. The winners of the second round play each other in a third round. This continues until there is a final winning team. There are no tie games; games are played into overtime if needed.

Answer 1

a. How many rounds of play are needed before a winner is determined? Explain your reasoning.

b. How many total games are played before a winner is determined? Explain your reasoning.

c. Suppose an additional round of play is added to the playoffs. How many teams would start in the playoffs? Explain your reasoning.

Answer 2

The number of surviving teams is halved each time, so are the number of games needed: 32, 16, 8, 4, 2, 1. From this you can determine total number of games, the rounds, and even how many teams you could add with another round.

Answer 3

a... Just count.
Number of games in each round: 32...16....8...4...2...1
How many rounds was that.

Answer 4

6?

Answer 5

yes.

Answer 6

is b 7?

Answer 7

b. No. In a 64 team tournament, a lot more than 7 games will be played.
I just wrote down the total number of games in each round above. What is the total number of games there?

Answer 8

63?

Answer 9

That's correct.
Or if you really want to impress your teacher, explain that there will be a loser in every game. Each team will lose 1 game...except the champion. That's 63 teams that will lose a game, and each game will involve 1 loser...therefore there are 63 games.

Answer 10

ok Thanks!! What about c