Question

Middle- earth is a fictional land inhabited by hobbits,
elves, dwarves and men. The hobbits and elves are peaceful
creatures that prefer slow, silent lives and appreciate nature
and art. The dwarves and the men engage in physical games. The
game is as follows. A tournament is one where out of the two
teams that play a match, the one that loses get eliminated.
The matches are played in different rounds, where in every
round; half of the teams get eliminated from the tournament.
If there are 8 rounds played in knock out tournament, how many
matches were played?

Answer 1

whats knock out tournament

Answer 2

there was one match played in the 8th round between the finalists
there were 2 matches played in the semifinals
there were 4 matches played in the quarter finals and so on.

Answer 3

got it?

Answer 4

options are a) 257 b) 256 c) 72 d) 255

Answer 5

Well, since there is one winner you know in round 8 only two teams remain, which means in the previous round, there were four teams (since if there were more, than more than two teams would remain), before that there must have been 8 teams for the same reason, and so on until you get back to round one. so:
round 8: 2
round 7: 4
round 6: 8
round 5: 16
round 4: 32
round 3: 64
round 2: 128
round 1: 256

In numerical terms, this is your general equation. T=2^(r) where T=amount of teams in the tournament and r=amount of rounds.

More specifically to your case, T=2^(8)
T=256
So, your final answer is at the beginning of the tournament, there were 256 teams.

Answer 6

yes got it
thanx

Answer 7

in round 8, 1 match was played
in round 7, 2 matches were played
in round 6, 4 matches were played
in round 5, 8 matches were played
in round 4, 16 matches were played
in round 3, 32 matches were played
in round 2, 64 matches were played
in round 1, 128 matches were played
add em all up.
ignore my previous answer.
I think you will get 255

Answer 8

My mistake, I misread the question, Dhatraditya's answer is the correct one.

Answer 9

i dont understand , if there are 4 teams in round 7, then who plays who?

Answer 10

so in round 7 there are 4 teams, how do they play against each other? 2 against 2?

Answer 11

suppose teams A and C were in the finals.
suppose teams A,B,C,D were in semifinals,
that means that A played B and won, which eliminated B
and C played D and won, eliminating D

Answer 12

so you have to just assume that they were matched properly

Answer 13

in every round , for every match, it is 1 team against 1 team

Answer 14

yup.

Answer 15

and the team that loses gets eliminated from the tournament.

Answer 16

so its like basketball , the college games

Answer 17

, it goes finals, semi finals, quarterfinals, ...

Answer 18

like this http://www.slate.com/id/2063215/

Answer 19

exactly. its the same concept as a march madness bracket

Answer 20

great job ;)

Answer 21

thanks :)

Answer 22

good