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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.
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n-1.
when each match is played a team gets eliminate so after 1st round n/2 teams remains
in next n/4and 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 leftand 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-1hence answer is n-1
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