Question

calculate no. of teams in each quarter if N=42

Answer 1

Explanation:

You just need to find out the nearest power of 2 greater than or equal to the total number of participants and subtract from it the number of participants. This will give you the number of bytes required. This is going to work for any number of participants, be it an odd number or a prime number.

For example, if there are 53 participants, nearest power of 2 greater than or equal to 53 is 64.

64−53=11

Thus you will need 11 byes. 42 teams will play the first round, out of which 21 will qualify and the 11 teams which got the byes will enter from this round. Thus there will be 32 teams in Round 2 and you can then go on like a normal knockout tournament because 32 is a power of 2.

This can also be done mathematically.

Let there be x teams and the closest power of two greater than or equal to x is 2n and y teams have to be given a bye.

x−y2 teams will qualify for round 2 and will face the y teams there

x−y2+y=2n−1

⟹x+y2=2n−1

⟹x+y=2n

⟹y=2n−x

Thus we get our result that number of byes equals nearest power of 2 minus the number of teams.

Answer 2

to know the teams in each quarter divide n by 4 = 42/4 the remainder is 2 so quarter 1 and 3 will have 1 team extra. each quarter will have 10 teams but quarter 1 and 3 will have 11 teams each.