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n-1 is the correct answer
After each match is played a team will get eliminated so after 1st round n/2 teams remain
in next n/4 will remain in tournament and so on…………..till one team remains.therefore
=n/2+n/4+…………+1
=1+2+4+…………..n/4+n/2
this is a Geometric Progression sequence with a=1 & r=2after each match, one team will get eliminated. thus after first round, n/2 teams are left.
after 2nd round , n/4 teams are leftThis implies after k th round
n/(2^k) teams are leftNow 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- 8523 views
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