Question

Arrange the following number of teams in a sequential order from less to more with respect to allotment of byes in a Knock-out Tournament :(A) 05
(B) 14
(C) 32
(D) 12
(E) 63

Choose the correct answer from the options given below :

• A. (C), (E), (B), (A), (D)
• B. (E), (C), (B), (D), (A)
• C. (C), (A), (D), (B), (E)
• D. (E), (B), (C), (A), (D)

Answer 1

The Correct Option is A

To arrange the number of teams in sequential order based on the number of byes in a Knock-out Tournament, we need to understand that the number of byes required is calculated by determining the next power of 2 greater than or equal to the number of teams. The difference between this power and the actual number of teams gives the number of byes. 

Steps:

1. Determine the next power of 2 greater than or equal to each number of teams.

2. Calculate the number of byes as the difference between this power of 2 and the number of teams.

Teams	Next Power of 2	Byes
05	8 (23)	8-5=3
14	16 (24)	16-14=2
32	32 (25)	32-32=0
12	16 (24)	16-12=4
63	64 (26)	64-63=1

3. Rank the teams by the number of byes in ascending order: 32 (0 byes), 63 (1 bye), 14 (2 byes), 5 (3 byes), 12 (4 byes).

The correct order based on the number of byes is: (C) 32, (E) 63, (B) 14, (A) 5, (D) 12.

Answer 2

The correct order for the number of byes required in a knockout tournament is based on the number of teams and the next highest power of 2. The goal is to ensure that the number of teams is adjusted to be a power of 2 for each round. The number of byes is calculated by subtracting the number of teams from the next power of 2. Here's the breakdown:

32 teams – No byes are required, as 32 is already a power of 2. This ensures a balanced competition with no need for automatic advances.

63 teams – The next highest power of 2 is 64, so 1 bye is needed to make the number of teams even for the first round.

14 teams – The next highest power of 2 is 16, so 2 byes are required to make the number of teams a power of 2.

5 teams – The next highest power of 2 is 8, so 3 byes are needed to make the number of teams even.

12 teams – The next highest power of 2 is 16, so 4 byes are required to ensure a balanced tournament structure.

This system of calculating byes ensures that each subsequent round can proceed with an even number of teams, maintaining a fair competition structure.