The disney Golf classic starts with 64 golfers. the golfes form pairs and each pair plays amtch. the losers drop out nad the winners of each pair then form new pairs and play again. Then those winners form pairs and play. this continues until there is one winner..

a- In how many mathches must the winner play
b- How many mtches are played by all the golers, to determine the winner?

round 1 : 32 games

round 2 : 16 games
round 3 : 8 games
round 4 : 4 games
round 5 : 2 games
final : 1 game

does that help you answer your question?

no it does nt. give me answer in clear numbers!

a) In order to determine the number of matches the winner must play, we can notice that there will be a total of 32 matches in the first round (64/2 = 32), as each pair will play against one another.

In each subsequent round, the number of matches is halved. Therefore, in the second round, there will be 16 matches (32/2 = 16), in the third round there will be 8 matches (16/2 = 8), and so on.

This pattern continues until there is only one match left, and that match determines the winner. Therefore, the winner must play a total of:
32 + 16 + 8 + 4 + 2 + 1 = 63 matches.

b) To determine the total number of matches played by all the golfers, we need to sum up the matches played in each round. Considering there are 64 golfers at the start, and each match eliminates one golfer, the number of matches played in each round will be the same as the number of eliminated golfers.

In the first round, there are 32 matches (64/2 = 32), and 32 golfers are eliminated.
In the second round, there are 16 matches (32/2 = 16), and 16 golfers are eliminated.
In the third round, there are 8 matches (16/2 = 8), and 8 golfers are eliminated.
This pattern continues until there is only one match left.

To calculate the total number of matches played, we can add up the matches played in each round:
32 + 16 + 8 + 4 + 2 + 1 = 63 matches.

Therefore, all the golfers in the Disney Golf Classic would play a total of 63 matches to determine the winner.

To answer these questions, we can break down the process step by step:

Step 1: In the first round, 64 golfers form 32 pairs. Each pair plays 1 match, and there must be a winner and a loser in each match. Since the losers drop out, we're left with 32 winners.

Step 2: In the second round, the 32 winners from the first round form 16 new pairs. Again, each pair plays 1 match, resulting in 16 winners.

Step 3: In the third round, the 16 winners from the second round form 8 new pairs. Each pair plays 1 match, resulting in 8 winners.

Step 4: This process continues until we have only 1 winner. The number of winners is halved, and thus the number of matches is halved in each round until we have the final winner.

Now we can answer the specific questions:

a) In how many matches must the winner play?
Since the number of matches is halved in each round, we can see that the winner plays 1 match in each round. As there are a total of 6 rounds (64, 32, 16, 8, 4, 2), the winner needs to play 6 matches to be crowned the champion.

b) How many matches are played by all the golfers to determine the winner?
To determine this, we need to sum up the matches played in each round:
Round 1: 32 matches (64 golfers / 2)
Round 2: 16 matches (32 golfers / 2)
Round 3: 8 matches
Round 4: 4 matches
Round 5: 2 matches
Round 6: 1 match

Adding all these matches together, we get: 32 + 16 + 8 + 4 + 2 + 1 = 63 matches.

Hence, all the golfers collectively play 63 matches to determine the winner.