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A total of 512 players participated in a single tennis knock

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A total of 512 players participated in a single tennis knock [#permalink] New post 01 May 2012, 20:26
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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!
[Reveal] Spoiler: OA
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Re: A total of 512 players participated in a single tennis knock [#permalink] New post 01 May 2012, 22:00
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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

However, the correct answer given is A 511, can anyone please exlain what's wrong in my approach? Thanks!


You've done everything right except calculation: 256+128+64+32+16+8+4+2+1=511.

Answer: A.

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Re: A total of 512 players participated in a single tennis knock [#permalink] New post 19 Nov 2012, 18:17
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There are 512 players, only 1 person wins, 511 players lose. in order to lose, you must have lost a game.

511 games.
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Re: A total of 512 players participated in a single tennis knock [#permalink] New post 26 Feb 2013, 18:12
1- the 512 players will play 256 games --> 256 plyers will go out from these games
2- the remaining is 256 players, they will play 128 games --> 128 players will go out
3- the remaining is 128 players, they will play 64 games --> 64 players will go out
4- the remaining is 64 players, they will play 32 games --> 32 players will go out
5- the remaining is 32 players, they will play 16 games --> 16 players will go out
6- the remaining is 16 players, they will play 8 games --> 8 players will go out
7- the remaining is 8 players, they will play 4 games --> 4 players will go out
8- the remaining is 4 players, they will play 2 games --> 2 players will go out.
9- the remaining is 2 players, they will play 1 games --> 1 players will go out

265+128+64+32+16+8+4+2+1=511
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Re: A total of 512 players participated in a single tennis knock [#permalink] New post 27 Feb 2013, 11:44
AlyoshaKaramazov wrote:
There are 512 players, only 1 person wins, 511 players lose. in order to lose, you must have lost a game.

511 games.


I know this is an old post. But damn, sometimes the answer is so simple, you just have to thinkg logically.

Thanks Alyosha
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Re: A total of 512 players participated in a single tennis knock [#permalink] New post 24 Jun 2013, 07:23
If you divide 512 by 2 recursively to factor: 512,256,128,64,32,16,8,4,2,1. so the answer narrows to down to either A or B.
Since the last dividend is 1, the sum will be odd so it should be 511

A
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Re: A total of 512 players participated in a single tennis knock [#permalink] New post 26 Dec 2013, 12:05
Bunuel 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

However, the correct answer given is A 511, can anyone please exlain what's wrong in my approach? Thanks!


You've done everything right except calculation: 256+128+64+32+16+8+4+2+1=511.

Answer: A.


Geometric progression

512 = 2^9

2^1 + 2^2 ....+2^9 + 1

2 ( 2^8-1) = 2^9 - 2 + 1

A is our friend here

Cheers!
J :)
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Re: A total of 512 players participated in a single tennis knock [#permalink] New post 03 Jan 2014, 16:34
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

However, the correct answer given is A 511, can anyone please exlain what's wrong in my approach? Thanks!



256+128+ 64+32+16+8+4+2+1
= 511
OA - A

Thanks for posting
:-D

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Re: A total of 512 players participated in a single tennis knock   [#permalink] 03 Jan 2014, 16:34
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