Swtiches for floor – 8,9,10 – in the elevator is broken.

n = number of teams,
x = a variable

When n is in order of 2^x,

for example, n = 2^4 = 16, then number of matches will be n-1 = 16-1 = 15 (simple GP)

But when n is not in order of 2^x,

for example, n = 21,

then number of matches will be n-1 = 21-1 = 20???

Lets check this, n = 21 = 16 + 5 = 16 + 4 + 1 (all in order of 2^x like, 2^4+2^2+2^0)

when n is in order of 2^x, then i can use n-1 for finding the matches.

for 16 teams = 15 matches
for 4 teams = 3 matches
for 1 team = 0 match

winner of these 2 groups needs to play again, along with the remaining 1 team. (total 3 teams remaining, say N)….

hence, N = 3 = 2+1 (again in order of 2^x)

for 3 teams = 2 matches are required for deciding the winner, who is none but the winner of all 21 teams.

Total matches to decide a winner =15+3+2 = 20 matches. that is (n-1).

Genarilized solution will be n-1.