Question

There are 11 teams participating in a Knock-out Tournament. Explain the procedure to calculate number of 'Byes' and also with the help of diagram allot 'Byes'.

Answer 1

Procedure:

Total Number of Teams: N = 11

Calculation of Byes:

Number of Byes = 2ⁿ − N

Here, the next higher power of 2 is 16.

= 16 − 11 = 5 Byes

Division of Teams

Since the number of teams is odd,

Upper Half:

\[ \frac{N+1}{2}=\frac{11+1}{2}\] = 6 Teams

Lower Half:

\[ \frac{N-1}{2}=\frac{11-1}{2}\] = 5 Teams

Distribution of Byes

Upper Half Byes:

\[ \frac{N_b-1}{2}=\frac{5-1}{2}\] = 2 Teams

Lower Half Byes:

\[ \frac{N_b+1}{2}=\frac{5+1}{2}\] = 3 Byes

Total Matches and Rounds:

\[ \text{Total Matches}=N-1=11-1\] = 10

\[ \text{Total Rounds}\] = 4