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akky8055 loves solving puzzles at PuzzleFry.com. I am proud PuzzleFry member and like my time invested in solving brain teasers.
  • n-1.
    when each match is played a team gets eliminate so after 1st round n/2 teams remains
    in next  n/4

    and so on
    till one team remains.
    therefore
    =n/2+n/4+…………+1
    =1+2+4+………….._n/4+n/2
    this is a GP sequence
    a=1 r=2
    and no. of terms = x(assumed)

    after each match, one team is eliminated. thus after first round, n/2 teams are left.
    after 2nd round , n/4 teams are left

    and so on

    after k th round

    n/(2^k) teams are left

    Now for n/(2^k)=1 team
    n=2^k
    k=log(n)
    a=1
    r=2
    k=log n (base 2)

    total matches = a(r^n – 1)/(r-1)
    =2^(log n) -1
    =n-1

    hence answer is n-1

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