Question

Anita prepared a fixture based on the league competition. She distributed this fixture to the coaches of all the teams. When Khushi received this fixture, it was misprinted and showed only the matches of rounds three and four. Study the fixture given below:
III Round
5 Bye
4 6
3 7
2 1
IV Round
4 Bye
3 5
2 6
1 7
Based on the above fixture and your previous knowledge answer the following questions:
(i) In which round the match between number 4 and 3 teams will be held?
(ii) How many rounds will be played in the tournament?
(A) 6 (B) 7 (C) 5 (D) 4
(iii) In which round team number 2 will get a bye?
(iv) How many matches will be played in the above fixture?
(A) 21 (B) 23 (C) 19 (D) 18
OR
(iv) The other name for a league tournament is _____.
(For Visually Impaired Candidates only - Alternative case on Keshav organising State level Kabaddi tournament with four committees)
(i) Which of the following committee is responsible for publishing the news?
(A) Technical committee (B) Finance committee (C) Logistics committee (D) Marketing committee
(ii) Which committee is responsible for maintaining the play fields while organising the tournament?
(A) Marketing committee (B) Logistics committee (C) Finance committee (D) Technical committee
(iii) Write any 2 post sports event responsibilities of finance committee?
OR
(iii) Purchase of sports equipment is a function of the \underline{\hspace{2cm}} committee.
(A) Logistics (B) Finance (C) Marketing (D) Technical
(iv) \underline{\hspace{2cm}} committee arranges refreshments, boarding and lodging. }

Hint:

In a cyclic league fixture with an odd number of teams, the number of rounds is always equal to the number of teams ($n$). If the number of teams is even, the number of rounds is $n-1$.

Answer 1

Step 1: There are \( n = 7 \) teams, odd, so the tournament runs for exactly \( n = 7 \) rounds with one bye per round; comparing Round III, Bye 5; 4-6, 3-7, 2-1, to Round IV, Bye 4; 3-5, 2-6, 1-7, shows every number drops by 1 each round, wrapping 1 to 7.

Step 2: Applying that shift both forward and backward rebuilds the full schedule: Round I, Bye 7; 1-6, 2-5, 3-4, Round II, Bye 6; 1-4, 2-3, 5-7, Round V, Bye 3; 1-5, 2-4, 6-7, Round VI, Bye 2; 1-3, 4-7, 5-6, Round VII, Bye 1; 2-7, 3-6, 4-5.

Step 3: Reading the table off directly: (i) team 4 vs team 3 falls in Round I; (ii) total rounds = 7, option (B); (iii) team 2's bye falls in Round VI; (iv) total matches, option (A); OR (iv) a league tournament is also called the Round Robin or Berger System. \[ \dfrac{n(n-1)}{2} = \dfrac{7 \times 6}{2} = \boxed{21} \]

Step 4: For the visually-impaired alternative on Keshav's committees: (i) publishing news is handled by the Marketing committee (D); (ii) maintaining play fields is handled by the Technical committee (D); (iii) post-event finance duties include preparing the audited financial report and clearing outstanding dues to vendors and officials, OR purchase of equipment falls under the Finance committee (B); (iv) arranging refreshments, boarding and lodging is handled by the Logistics committee.