draw a fixture of 21 teams in which 4 teams are seeded
Answers
Answer:
N=21 Upper half=n+1/2=21+1/2=22/2=11 Lower half=n-1/2=21-1/2=20/2=10 No. Of matches =n-1=21-1=20 Seeding=4 No.of team for bye=21-4=17 No.of bye =p2-n P2=2*2*2*2*2=32 No. Of bye=32-21=11 Upper half byes=NB-1/2=11-1/2=10/2=5 Lower half byes=NB+1/2=11+1/2=12/2=6 No.of rounds=5 No. Of teams,seeding and byes in quarters = Q1=teams=5+1,seeding=1,byes=2 Q2=teams=5,seeding=1,byes=3 Q3=teams=5,seeding=1,byes=3 Q4=teams=5,seeding=1,byes=3 After that make fixtures.
Explanation:
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Drawing the fixture will include 5 rounds, 11 byes including 4 seedings.
Given:
No of teams = 21
No of teams seeded = 4
To find:
A fixture for 21 teams where 4 teams specially seeded
Solution:
Number of team = N = 21
Teams in the upper half = (N + 1)/2 = (21 + 1)/2 = 22/2 = 11
Teams in the lower half = (N - 1)/2 = (21 - 1)/2 = 20/2 = 10
Special seeding is where the teams receive an advantage of not playing the first round and receive direct entry to the next round.
No of teams seeded = 4
Byes are where the team qualifies for the next round. Some teams are given byes directly and some have the possibility of getting a bye if they win their match.
Since we have 5 rounds and two teams play against each other so 2 x 2 x 2 x 2 x 2 = 32
No of byes including the seeding of 4 teams = 32 - 21 = 11
Byes in the upper half = (teams in upper half - 1)/2
= (11 - 1)/2
= 5
Bye in the lower half = (teams in lower half + 1)/2
= (11 + 1)/ 2
= 6
The number of rounds is 5. These five rounds include two rounds of elimination of teams, quarter-finals, Semi-finals, and Finals.
No of teams, seeding, and byes = Q1 = 5+1
Seeding = 1 and Byes = 2
No of teams, seeding, and byes = Q2, Q3, Q4 = 5
Seeding = 1 and Byes = 3
From the above information, the diagram is attached below.
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