Sevnety-eight players entered a single elimination tennis tournament.How many matches were played to determine the overall champ?
please help me...and if u get the answer can you explain how you got it with a rule or a pattern
To determine the number of matches in a single elimination tournament, we can use the concept of rounds. In each round, half of the players are eliminated until there is one overall champion.
In the first round, half of the players are eliminated. So, out of the 98 players, 49 matches are played. This is because each match eliminates one player, and we need to eliminate 49 players to proceed to the next round.
In the second round, again half of the players are eliminated. Now we are left with 49 players. Similarly, 24 matches are played in this round to eliminate 24 players.
This process continues until we have only one player left, who is the overall champion. Since we are halving the number of players in each round, we can calculate the total number of matches by summing the matches played in each round.
Here is a breakdown of the number of matches in each round:
Round 1: 49 matches
Round 2: 24 matches
Round 3: 12 matches
Round 4: 6 matches
Round 5: 3 matches
Round 6: 2 matches
Round 7: 1 match (final)
Adding up these numbers, we get a total of 49 + 24 + 12 + 6 + 3 + 2 + 1 = 97 matches.
Therefore, to determine the overall champion in a single elimination tennis tournament with 98 players, 97 matches need to be played.