Question
While specifying all calculations, prepare a 'knock-out fixture' for 19 teams.
✓
Answer
Solution:Total number of teams = 19
total number of matches = 19 - 1 = 18
Number of teams in the upper half.
$=\frac{\text{N}+1}{2}=\frac{19+1}{2}=\frac{20}{2}=10\ \text{teams}$
Number of teams in the lower half.
$=\frac{\text{N}-1}{2}=\frac{19-1}{2}=\frac{18}{2}=9\ \text{teams}$
Total number of boys.
$=32 - 19=13\ \text{Byes}$
Number of byes in the upper half.
$\frac{\text{NB}-1}{2}=\frac{13-1}{2}=\frac{12}{2}=6\ \text{byes}$
Number of byes in the lower half.
$\frac{\text{NB}+1}{2}=\frac{13+1}{2}=\frac{14}{2}=7\ \text{byes}$
Number of rounds
$=2\times 2\times 2\times2\times 2=5\ \text{rounds}$
Teams in each quarter:
= I Quarter = Q + 1 = 4 + 1 = 5 teams.
= II Quarter = Q + 1 =4 + 1 = 5 teams.
= III Quarter = Q + 1 = 4 + 1 = 5 teams.
= IV Quarter = Q + 4 = 4 teams.
total number of matches = 19 - 1 = 18
Number of teams in the upper half.
$=\frac{\text{N}+1}{2}=\frac{19+1}{2}=\frac{20}{2}=10\ \text{teams}$
Number of teams in the lower half.
$=\frac{\text{N}-1}{2}=\frac{19-1}{2}=\frac{18}{2}=9\ \text{teams}$
Total number of boys.
$=32 - 19=13\ \text{Byes}$
Number of byes in the upper half.
$\frac{\text{NB}-1}{2}=\frac{13-1}{2}=\frac{12}{2}=6\ \text{byes}$
Number of byes in the lower half.
$\frac{\text{NB}+1}{2}=\frac{13+1}{2}=\frac{14}{2}=7\ \text{byes}$
Number of rounds
$=2\times 2\times 2\times2\times 2=5\ \text{rounds}$
Teams in each quarter:
= I Quarter = Q + 1 = 4 + 1 = 5 teams.
= II Quarter = Q + 1 =4 + 1 = 5 teams.
= III Quarter = Q + 1 = 4 + 1 = 5 teams.
= IV Quarter = Q + 4 = 4 teams.
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