Question

A soccer league has 64 teams competing in a tournamentIn each round of pairs of teams compete the team that wins advances to the next round of the table below shows the results of the first two rounds

At the end which round Weatherby only two teams remaining assuming there will be no ties

A. Round 4
B. Round 5
C. Round 6
D. Round 7

Answer 1

Total teams = 64

After round 1, teams remaining = 64 ÷ 2 = 32

After round 2, teams remaining = 32 ÷ 2 = 16 = or (64 ÷ 2^2 = 16)

After round n, teams remaining = 64 ÷ (2^n)

Let after n rounds, teams remaining = 2

=> 64 ÷ 2^n = 2

=> 64/(2^n) = 2

=> 64/2 = 2^n

=> 32 = 2^n

=> 2^5 = 2^n

=> n = 5

Thus, after round 5, two teams will remain.