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tennis knock out tournament - number of matches ?

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by GMIHIR » Tue May 01, 2012 9:00 pm
A total of 512 players participated in a single tennis knock out tournament.
What is the total number of matches played in the tournament?
(Knockout means if a player loses, he is out of the tournament). No match ends in a tie.
A 511

B 512

C 256

D 255

E 1023

I chose D, solved this way - after first 256 matches, remaing players 256 (those 256 who lost are knocked out), after another 128 matches, remaining players are 128, after 64 more matches, no of remainig players are 64, after 32, 32, after 16, 16, after 8, 8, after 4, 4, after 2,2, and then 1 -
total 256 + 128+64+32+16+8+1 = 255 matches

However, the correct answer given is A 511, can anyone please exlain what's wrong in my approach? Thanks!
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by niketdoshi123 » Tue May 01, 2012 9:23 pm
Your approach was right but you made calculation blunder.
256+128+64+32+16+8+4+2+1 = 511
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by tpr-becky » Wed May 02, 2012 10:36 am
Yes, it was just the calculation that was incorrect - remember to check calculations with common sense and it may be good to use a process of elimination strategy instead of focusing solely on the calculation. For instance in this problem you correctly inferred that the first match woudl have 256 games - that means total games must be more than that. this woudl eliminate answers C and D - also if each match has 1/2 the games of the previous match you are going to have a hard time getting to something over 1000 so that eliminates E.

511 and 512 are very close so you will probably have to calculate but you could eliminate this by realizing that each match will have an even number of games until you get to the final match (which will be 1) and therefore the answer must be odd.

Remember the GMAT is not testing your raw calculation ability and sometimes it is faster, and causes fewer errors, if you learn to work through the problem solving logic and more basic math concepts.

Best of Luck.
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by sanju09 » Thu May 03, 2012 4:53 am
GMIHIR wrote:A total of 512 players participated in a single tennis knock out tournament.
What is the total number of matches played in the tournament?
(Knockout means if a player loses, he is out of the tournament). No match ends in a tie.
A 511

B 512

C 256

D 255

E 1023

I chose D, solved this way - after first 256 matches, remaing players 256 (those 256 who lost are knocked out), after another 128 matches, remaining players are 128, after 64 more matches, no of remainig players are 64, after 32, 32, after 16, 16, after 8, 8, after 4, 4, after 2,2, and then 1 -
total 256 + 128+64+32+16+8+1 = 255 matches (OMG)

However, the correct answer given is A 511, can anyone please exlain what's wrong in my approach? Thanks!
Whenever x players participate in a knock out tournament such as this (No match ends in a tie), where x is an even positive integer, the total number of matches played is given by x - 1. Have fun...
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by Brent@GMATPrepNow » Thu May 03, 2012 6:19 am
GMIHIR wrote:A total of 512 players participated in a single tennis knock out tournament.
What is the total number of matches played in the tournament?
(Knockout means if a player loses, he is out of the tournament). No match ends in a tie.
A 511
B 512
C 256
D 255
E 1023
Every game results in a player getting knocked out of the tournament.
We want to knock out 511 players so that one player (the tournament winner) remains.
To knock out 511 players, we need to play 511 games.

Answer=A

Note: This approach works for any number of participants in a single-knockout tournament. It doesn't matter if there is an even or an odd number of participants.

Cheers,
Brent
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by parveen110 » Mon Feb 24, 2014 4:27 am
Brent@GMATPrepNow wrote:
GMIHIR wrote:A total of 512 players participated in a single tennis knock out tournament.
What is the total number of matches played in the tournament?
(Knockout means if a player loses, he is out of the tournament). No match ends in a tie.
A 511
B 512
C 256
D 255
E 1023
Every game results in a player getting knocked out of the tournament.
We want to knock out 511 players so that one player (the tournament winner) remains.
To knock out 511 players, we need to play 511 games.

Answer=A

Note: This approach works for any number of participants in a single-knockout tournament. It doesn't matter if there is an even or an odd number of participants.

Cheers,
Brent
Hi Brent,

Please explain, why will it work for even and odd number of participants? If, suppose, 511 players sign up for the tournament then there will be 250 pairs. What happens to the player left out? Does he get promoted to the next round without actually playing the first round? If so, it will continue till the end? I'm really at sea over here. Please help.

Thanks!
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by Brent@GMATPrepNow » Mon Feb 24, 2014 7:07 am
parveen110 wrote: Hi Brent,

Please explain, why will it work for even and odd number of participants? If, suppose, 511 players sign up for the tournament then there will be 250 pairs. What happens to the player left out? Does he get promoted to the next round without actually playing the first round? If so, it will continue till the end? I'm really at sea over here. Please help.

Thanks!
Hi Parveen110,

This kind of thing happens all of the time. In fact, lots of tournaments don't have a power of 2 (e.g., 8, 16, 32, 64 etc.) for the number of participants. So, don't concern yourself with the concepts of rounds, since the question doesn't ask us about this.

For example, how would we handle a single knockout tournament with 3 people?
Well, first 2 of the people would need to play a match. At the end of that match, the loser goes home.
At this point, there are 2 people remaining. Once they play their match, the loser goes home, and there's one player remaining, and this person wins the tournament.
So, when there are 3 players, 2 matches are required to crown the champion.

What's important here is that EACH match results in a player going home.
So, if there are 511 players in the tournament, then after 510 matches, all of the players BUT ONE will have gone home. The one remaining player will be champion.

Cheers,
Brent
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by Abhishek009 » Mon Feb 24, 2014 9:05 am
sanju09 wrote:
GMIHIR wrote:A total of 512 players participated in a single tennis knock out tournament.
What is the total number of matches played in the tournament?
(Knockout means if a player loses, he is out of the tournament). No match ends in a tie.
A 511

B 512

C 256

D 255

E 1023

I chose D, solved this way - after first 256 matches, remaing players 256 (those 256 who lost are knocked out), after another 128 matches, remaining players are 128, after 64 more matches, no of remainig players are 64, after 32, 32, after 16, 16, after 8, 8, after 4, 4, after 2,2, and then 1 -
total 256 + 128+64+32+16+8+1 = 255 matches (OMG)

However, the correct answer given is A 511, can anyone please exlain what's wrong in my approach? Thanks!
Whenever x players participate in a knock out tournament such as this (No match ends in a tie), where x is an even positive integer, the total number of matches played is given by x - 1. Have fun...

Excellent shortcut tips provided would like to enhance it a bit further...


Suppose there are 2 players A and B competing in a knockout match , so Number of possible matches is -

A Vs B

Answer is Only One.

Suppose there are 3 players A , B and C competing in a knockout match , so Number of possible matches is -

A Vs B , and A/B( Whowver wins with plays with C) vs C

Suppose there are 3 players A , B , C & D competing in a knockout match , so Number of possible matches is -

A Vs B , C Vs D

A/B Vs C/D { Whoever Wins plays with the other team , similar to World Cup Matches )


Thus the General Observations is -

When there are 2 teams - 1 Match

When there are 3 teams - 2 Matches

When there are 4 teams - 3 Matches

When there are n teams - ( n - 1 ) Matches


Hence when there are 512 Teams there will be 511 matches.
Abhishek
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by Nupur.nk » Mon Feb 24, 2014 1:23 pm
Abhishek009 wrote:
sanju09 wrote:
GMIHIR wrote:A total of 512 players participated in a single tennis knock out tournament.
What is the total number of matches played in the tournament?
(Knockout means if a player loses, he is out of the tournament). No match ends in a tie.
A 511

B 512

C 256

D 255

E 1023

I chose D, solved this way - after first 256 matches, remaing players 256 (those 256 who lost are knocked out), after another 128 matches, remaining players are 128, after 64 more matches, no of remainig players are 64, after 32, 32, after 16, 16, after 8, 8, after 4, 4, after 2,2, and then 1 -
total 256 + 128+64+32+16+8+1 = 255 matches (OMG)

However, the correct answer given is A 511, can anyone please exlain what's wrong in my approach? Thanks!
Whenever x players participate in a knock out tournament such as this (No match ends in a tie), where x is an even positive integer, the total number of matches played is given by x - 1. Have fun...

Excellent shortcut tips provided would like to enhance it a bit further...


Suppose there are 2 players A and B competing in a knockout match , so Number of possible matches is -

A Vs B

Answer is Only One.

Suppose there are 3 players A , B and C competing in a knockout match , so Number of possible matches is -

A Vs B , and A/B( Whowver wins with plays with C) vs C

Suppose there are 3 players A , B , C & D competing in a knockout match , so Number of possible matches is -

A Vs B , C Vs D

A/B Vs C/D { Whoever Wins plays with the other team , similar to World Cup Matches )


Thus the General Observations is -

When there are 2 teams - 1 Match

When there are 3 teams - 2 Matches

When there are 4 teams - 3 Matches

When there are n teams - ( n - 1 ) Matches


Hence when there are 512 Teams there will be 511 matches.
I did something similar...observation !

When there are 4 players, the total number of matches played are 3, because:

A B C D = 4 players

A plays with B, B loses B is out
A plays with C, C loses C is out
A plays with D, D loses D is out

Thus three matches are played.

So with 512 players, 511 matches are played !
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by Nupur.nk » Mon Feb 24, 2014 1:23 pm
Abhishek009 wrote:
sanju09 wrote:
GMIHIR wrote:A total of 512 players participated in a single tennis knock out tournament.
What is the total number of matches played in the tournament?
(Knockout means if a player loses, he is out of the tournament). No match ends in a tie.
A 511

B 512

C 256

D 255

E 1023

I chose D, solved this way - after first 256 matches, remaing players 256 (those 256 who lost are knocked out), after another 128 matches, remaining players are 128, after 64 more matches, no of remainig players are 64, after 32, 32, after 16, 16, after 8, 8, after 4, 4, after 2,2, and then 1 -
total 256 + 128+64+32+16+8+1 = 255 matches (OMG)

However, the correct answer given is A 511, can anyone please exlain what's wrong in my approach? Thanks!
Whenever x players participate in a knock out tournament such as this (No match ends in a tie), where x is an even positive integer, the total number of matches played is given by x - 1. Have fun...

Excellent shortcut tips provided would like to enhance it a bit further...


Suppose there are 2 players A and B competing in a knockout match , so Number of possible matches is -

A Vs B

Answer is Only One.

Suppose there are 3 players A , B and C competing in a knockout match , so Number of possible matches is -

A Vs B , and A/B( Whowver wins with plays with C) vs C

Suppose there are 3 players A , B , C & D competing in a knockout match , so Number of possible matches is -

A Vs B , C Vs D

A/B Vs C/D { Whoever Wins plays with the other team , similar to World Cup Matches )


Thus the General Observations is -

When there are 2 teams - 1 Match

When there are 3 teams - 2 Matches

When there are 4 teams - 3 Matches

When there are n teams - ( n - 1 ) Matches


Hence when there are 512 Teams there will be 511 matches.
I did something similar...observation !

When there are 4 players, the total number of matches played are 3, because:

A B C D = 4 players

A plays with B, B loses B is out
A plays with C, C loses C is out
A plays with D, D loses D is out

Thus three matches are played.

So with 512 players, 511 matches are played !
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