Grandmother needs help with Math problem!

[jackemail]

Trying to help 6th grader with Math homework...we have all of them but one problem. For some reason, this one is stumping both of us. No matter how we work it, we end up with one player left over. Anyone help?

78 players entered a single elimination tennis tournament. How many matches were played to determine the overall champ? How did you arrive at the answer?

Thanks for any help!

 

[Lisa loves Pooh]

78 people, first match, there are 78/2 games, thus 39 games. 39 people eliminated, 39 people left.

Next match, you have 39/2 games...or 19 games with 1 person sitting out. He "wins". 19 people eliminated, with 19 winners + the 1 person that sat out or 20 people left.

Then 10 matches, 5 lose, 5 winners left...

2 matches + 1 left over, 2 win plus the one left = 3 left..

2 play, 1 left plus the 1 hanging out---leads to final game...

Final game--winner.

So I have 6 rounds...but I know nothing about single elimination or if that is correct. (Oh wait--you said matches...so that was 39 + 19 +10 + 2 + 1 + 1 = 72 matches still no idea if that is correct)

Not sure what the algebraic equation would be either. (ETA again: But interesting that if you take the total number of people and subtract the 6 rounds, you get 72...probably just a coincidence or my math error.)

 

[princessmom29]

Trying to help 6th grader with Math homework...we have all of them but one problem. For some reason, this one is stumping both of us. No matter how we work it, we end up with one player left over. Anyone help?

78 players entered a single elimination tennis tournament. How many matches were played to determine the overall champ? How did you arrive at the answer?

Thanks for any help!

here goes:
In a single elimination tourney, half the players are eliminated each round so:
after round 1: 39 left, one player will have a bye the next round
after round 2: 38 players play, half of those continue on plus the player with a bye so 20 left. Non one has a bye in round 3
after round 3: 10 left
after round 4: 5 left, one gets a bye next round
after round 5: 4 players play so 2 left, plus the bye makes 3, one btes to the next round
after round six: 2 play, one of those advance plus the bye so round 6 would decide the winner.
It takes six rounds to get a winner.

 

[timmac]

No need for any fancy math for this one.... there's 78 players and it's single elimination. Each match that is played eliminates exactly one player. There is exactly one winner. Therefore there are 78 - 1 = 77 people who have to be eliminated... which takes exactly 77 matches.

 

[thegales]

If each player is eliminated after one loss (single elimination), then the number of matches is one less than the number of players.

It does not matter how the games are played. You can only have as many games as you have losers.


(Edited to add that I see timmac beat me to it)

 

[timmac]

here goes:
In a single elimination tourney, half the players are eliminated each round so:
after round 1: 39 left, one player will have a bye the next round
after round 2: 38 players play, half of those continue on plus the player with a bye so 20 left. Non one has a bye in round 3
after round 3: 10 left
after round 4: 5 left, one gets a bye next round
after round 5: 4 players play so 2 left, plus the bye makes 3, one btes to the next round
after round six: 2 play, one of those advance plus the bye so round 6 would decide the winner.
It takes six rounds to get a winner.

Careful... round 6 yields a winner and a bye... round 7 is the final match between those 2.

 

[jackemail]

Getting it now!!! THANK YOU!!!!!

 

[npcougar]

Round one: 39 matches 78 people at 2 per match
Round two: 19 matches 1 bye 39 people at 2 per match
Round three: 10 matches 20 people at 2 per match
Round four: 5 matches 10 people at 2 per match
Round five: 2 matches 1 bye 5 people at 2 per match
Round six: 1 match 1 bye 3 people at 2 per match
Round seven: 1 match 2 people at 2 per match
1 winner

77 matches

 

[jackemail]

Y'all are the best! We blazed through all the other problems, but this last one had us, for some reason....maybe trying to make it harder than it was.

Thanks for your time and assistance.

 

[Lisa loves Pooh]

Clearly I missed a roUnd.

 

[dis-happy]

Draw sheets don't look like that.
(you'd have to start with a round of 128 and it goes by halves after that).

And I don't think you're allowed to have a bye after the quarterfinals round.


signed,
tennis mom

 

[DeaverTex]

Good thing that the teacher didn't specify double elimination with a wrap-around bye. (Those make my head hurt.)