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: Understanding the Concept:
By observing the fixture, we see that the numbers are rotating in a Cyclic Method. In this method, one team (or 'Bye') is fixed at the top right, and others rotate clockwise. Since team numbers up to 7 are mentioned, there are $n = 7$ teams. Because 7 is an odd number, the number of rounds is $n = 7$, and one team gets a 'Bye' in each round.
Step 2: Key Formula or Approach:

1. Total Rounds (for odd $n$) $= n$.

2. Total Matches $= \frac{n(n-1)}{2}$.

3. In Cyclic rotation, if $n$ is odd, 'Bye' is fixed and numbers rotate.
Step 3: Detailed Explanation:

1. (i) Round for Match 4 vs 3: Following the cyclic pattern (where numbers shift one position clockwise each round), if Round IV is [4-Bye, 3-5, 2-6, 1-7], in Round V the Bye goes to
3. In Round VI the Bye goes to
2. In Round VII, the pairing would be [Bye-1, 7-2, 6-3, 5-4]. Thus, the match between 4 and 3 is in Round VII.
2. (ii) Total Rounds: Since $n = 7$ (odd), Rounds $= 7$. Correct Option: (B) 7.
3. (iii) Round for Team 2 Bye: In this pattern, the 'Bye' moves sequentially through the numbers. Round III (5-Bye), Round IV (4-Bye), Round V (3-Bye). Therefore, in Round VI, Team 2 will get a 'Bye'.
4. (iv) Total Matches: $\frac{7(7-1)}{2} = \frac{7 \times 6}{2} = 21$. Correct Option: (A) 2
1.
5. OR (iv) Other name: The other name for a league tournament is the Berger System (or Round Robin).
Step 4: Final Answer:
(i) Round VII (ii) (B) 7 (iii) Round VI (iv) (A) 21 OR (iv) Berger System. % Visually Impaired Candidates Section For Visually Impaired Candidates Only:
Step 5: Explanation for Committee Questions:

1. (i) Publishing News: This is a promotional task handled by the (D) Marketing committee (specifically the publicity sub-committee).
2. (ii) Maintaining Playfields: This involves the technical setup and rules of the game, handled by the (D) Technical committee.
3. (iii) Post-event Finance Duties: (a) Preparation of the final balance sheet and financial report. (b) Making final payments to vendors and settling all outstanding bills.
4. OR (iii) Purchase of Equipment: Handled by the (B) Finance committee (as it involves fund allocation and procurement).
5. (iv) Refreshments/Lodging: This is the responsibility of the Logistics committee (specifically the boarding and lodging sub-committee).