Tournaments and CompetitionsClass 11 Health And Physical Education NCERT Solutions

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Q1I. Long Answer Questions

Draw a fixture for Single Knock-out Tournament with 11 teams.

Solution

To draw a fixture for 11 teams in a Single Knock-out Tournament, we first need to calculate the number of teams in each half, the number of byes, and the total number of matches.
Calculations:
  • Total Number of Teams (N) = 11
  • Next highest power of two = 16
  • Total Number of Matches = N - 1 = 11 - 1 = 10
  • Total Number of Byes (Nb) = 16 - 11 = 5
  • Number of Teams in Upper Half = (N + 1) / 2 = (11 + 1) / 2 = 6 teams
  • Number of Teams in Lower Half = (N - 1) / 2 = (11 - 1) / 2 = 5 teams
  • Number of Byes in Upper Half = (Nb - 1) / 2 = (5 - 1) / 2 = 2 byes
  • Number of Byes in Lower Half = (Nb + 1) / 2 = (5 + 1) / 2 = 3 byes
Procedure for giving byes:
  • 1st Bye: Last team of the lower half (Team 11)
  • 2nd Bye: First team of the upper half (Team 1)
  • 3rd Bye: First team of the lower half (Team 7)
  • 4th Bye: Last team of the upper half (Team 6)
  • 5th Bye: Team immediately above the first bye (Team 10)
Fixture:
UPPER HALF
Round I
  • Team 1 (Bye)
  • Team 2 vs Team 3 (Match 1)
  • Team 4 vs Team 5 (Match 2)
  • Team 6 (Bye)
LOWER HALF
  • Team 7 (Bye)
  • Team 8 vs Team 9 (Match 3)
  • Team 10 (Bye)
  • Team 11 (Bye)

Round II
UPPER HALF
  • Team 1 vs Winner of Match 1
  • Winner of Match 2 vs Team 6
LOWER HALF
  • Team 7 vs Winner of Match 3
  • Team 10 vs Team 11

Round III (Semi-Finals)
  • Winner of Upper Half (Round II) vs Winner of Upper Half (Round II)
  • Winner of Lower Half (Round II) vs Winner of Lower Half (Round II)

Round IV (Final)
  • Winner of Semi-Final 1 vs Winner of Semi-Final 2