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A total of 512 players participated in a single tennis knock [#permalink]
 01 May 2012, 21:26
Question Stats:
65% (02:10) correct
34% (01:09) wrong based on 11 sessions
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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Re: A total of 512 players participated in a single tennis knock [#permalink]
19 Nov 2012, 19:17
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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]
01 May 2012, 23:00
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]
26 Feb 2013, 19:12
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]
26 Feb 2013, 23:48
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! Apart form the calculation error which Bunuel pointed out, everything was spot on. However, for those who still struggle with such problems, it's always easier to scale down the level of the problem. Say there were only two players. Thus, only one match would be necessary. For three players, only 2 matches would be necessary. For 4 players, only 3 matches would be necessary. Thus for N players for the mentioned problem, only (N-1) matches are necessary.
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Re: A total of 512 players participated in a single tennis knock [#permalink]
27 Feb 2013, 12:44
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]
27 Feb 2013, 12:44
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