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
Usually in a single elimination, the number of players is a power of 2,
if not, there will have to be "byes".
e.g. the French Open has 128 starting competitors, or 2^7
You have 78 players, so the first round would have
39 matches with 39 remaining winners.
So there will have to be some rules stated for byes.
what ????this is so confusin
To determine the total number of matches played in a single elimination tournament, we can use the formula:
Total number of matches = Total number of players - 1
In this case, there are 98 players, so the total number of matches can be calculated as:
Total number of matches = 98 - 1
= 97
Therefore, a total of 97 matches were played to determine the overall champion in the tournament.
The rule or pattern behind this formula is that in a single elimination tournament, each match eliminates one player from the competition. As there can only be one overall champion at the end, all players except for the champion will be eliminated. Hence, the total number of matches will always be one less than the total number of players.
To determine how many matches were played in a single elimination tennis tournament with 98 players, we can use the fact that in each round, half the players get eliminated.
In the first round, 98 players participate. Since it's single elimination, half of them will be eliminated, which is 98/2 = 49 players.
In the second round, 49 players participate. Again, half of them will be eliminated, which is 49/2 = 24.5 players.
However, since we can't have half a player, we round up to the nearest whole number, which is 25 players.
In the third round, 25 players participate. Again, half of them will be eliminated, which is 25/2 = 12.5.
Again, we round up to the nearest whole number, which is 13 players.
In the fourth round, 13 players participate. Half of them will be eliminated, which is 13/2 = 6.5.
We round up to the nearest whole number, which is 7 players.
In the fifth round, 7 players participate. Half of them will be eliminated, which is 7/2 = 3.5.
Again, we round up to the nearest whole number, which is 4 players.
In the sixth round, 4 players participate. Half of them will be eliminated, which is 4/2 = 2 players.
In the final round, 2 players participate, and half of them will be eliminated, which is 2/2 = 1 player.
Therefore, the total number of matches played to determine the overall champion in a single elimination tennis tournament with 98 players is:
49 + 25 + 13 + 7 + 4 + 2 + 1 = 101 matches.