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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 manymatches were played?
  • a)
    257
  • b)
    256
  • c)
    72
  • d)
    255
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Middle- earth is a fictional land inhabited by hobbits, elves, dwarves...
Solution:

Given,
Number of rounds played = 8
Number of teams participating initially = 2^8 = 256

To find:
Number of matches played

Approach:
In every round, half of the teams get eliminated. Therefore, the number of teams remaining after each round can be calculated as follows:

Round 1: 256 teams
Round 2: 128 teams
Round 3: 64 teams
Round 4: 32 teams
Round 5: 16 teams
Round 6: 8 teams
Round 7: 4 teams
Round 8: 2 teams

As there are 2 teams left after round 8, the tournament is over. The number of matches played in every round is equal to the number of teams remaining after the previous round divided by 2.

Number of matches played in each round:

Round 1: 256/2 = 128
Round 2: 128/2 = 64
Round 3: 64/2 = 32
Round 4: 32/2 = 16
Round 5: 16/2 = 8
Round 6: 8/2 = 4
Round 7: 4/2 = 2
Round 8: 2/2 = 1

Total number of matches played = Sum of matches played in each round

= 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1

= 255

Therefore, the correct answer is option D) 255.
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Community Answer
Middle- earth is a fictional land inhabited by hobbits, elves, dwarves...
2^n-1=2^8-1=255
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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 manymatches were played?a)257b)256c)72d)255Correct answer is option 'D'. Can you explain this answer?
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