A total of 512 players participated in a single tennis knock

Question

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!

AlyoshaKaramazov · Accepted Answer

There are 512 players, only 1 person wins, 511 players lose. in order to lose, you must have lost a game.

511 games.

Bunuel · Answer

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

Answer: A.

aiha85 · Answer

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

amonsa · Answer

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

Thanks Alyosha

Reaper · Answer

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

jlgdr · Answer

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

rango · Answer

256+128+ 64+32+16+8+4+2+1 = 511 OA - A Thanks for posting :-D

georgesanjay · Answer

One of the best logics I've seen for these knockout questions is as follows:

In this question, there are 512 participants. And it takes ONE match to eliminate ONE player. So at the end of the day you need to eliminate everyone except the winner. ie. you need to eliminate 511 participants and naturally you need 511 matches for the same

Mathivanan Palraj · Answer

If there are 2 players, then there will be only 1 match
If there are 4 players, then there will be 2+1 matches
8 players, 4+2+1=7
16 players, 8+4+2+1 = 15
Now you are getting the pattern
512 players, 256+128+64+..+2+1=511

Abhishek009 · Answer

Good catch , or U can go the other way round - When there are 2 player only 1 knockout match is needed When there are 3 player only 2 knockout match is needed When there are 4 player only 3 knockout match is needed So, the pattern formed is - When there are n player only n - 1 knockout match is needed Hence , When there are 512 player only 511 (512 - 1 ) knockout match is needed Either way answer will be the same but the best thing/strategy is to solve the problems within minimum time & calculation :-D

stonecold · Answer

Firstly the question should state that a match is played between 2 players (what if its a cricket match)
assuming the match is played between 2 teams = > number of matches => 512/2 + 256/2 +128/2+64/2+32/2+16/2+8/2+4/2+2/2
we dont need to calculate the sum here => the unit digit will be 1 
SMASH that A

umg · Answer

1. Question mentions that it is a  Tennis Tournament  of  Singles .
2. All we know is that the sum is Odd. Please explain how will you get the unit's digit = 1 by looking at the sequence.

My Solution:

# of matches = 256 + 128 + 64 + ... + 2 + 1 =  2^8 + 2^7 + 2^6 + ... + 2^1 + 2^0  => Ascending G.P.

Sum of G.P. = \frac{a(r^n - 1)}{a-1} 
Where, 
a = First Term = 1 (Sum starts from 1)
r = Common Ratio = 2 (ratio of each successive term is 2)
n = Number of terms = 9

Therefore,
Sum =  \frac{1 * (2^9 - 1)}{2-1}  = 512 - 1 = 511

MathRevolution · Answer

Let there be player A who wins the tournament. He will beat the remaining 511 players to win.

So, 511 matches.

Answer A

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A total of 512 players participated in a single tennis knock

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