Q.Case Study 2: XYZ School is conducting an invitation tournament in which 25 teams have sent their entries. Matches have to be conducted on a knockout basis. a. How many total matches will be played?
b. How many matches will be played in the first round of the tournament?
c. How many rounds will be played?
d. Which team will get the 4th bye of the tournament?

Bye Determination

In a knockout tournament, every match must eliminate exactly one team, and the format works cleanly only when the number of teams in each round is a power of 2 — 2, 4, 8, 16, 32, and so on. The moment real entries come in, though, the count is rarely so tidy. If 11 teams register, you cannot pair them evenly in round one. Some teams must be given a free pass — called a bye — directly into the next round without playing, so that the field left to compete in round one still reduces to a power of 2.

How Many Byes Are Needed

The number of byes is fixed by one rule: take the next power of 2 above the number of teams, and subtract the number of teams from it.

Number of Byes = (next higher power of 2) − Number of teams

For 11 teams, the next power of 2 is 16, so the byes needed are 16 − 11 = 5. For 12 teams, the next power of 2 is 16, so byes = 16 − 12 = 4. For 19 teams, the next power of 2 is 32, so byes = 32 − 19 = 13. If the number of teams is already a power of 2 (say, 8 or 16), no byes are needed at all.

Splitting Byes Between the Two Halves

The fixture is drawn with the teams divided into an Upper Half and a Lower Half. If the byes come out to an even number, they are split equally between the two halves. If the byes come out odd, the Upper Half gets (Byes − 1)/2 and the Lower Half gets (Byes + 1)/2 — the Lower Half always receives the larger share when the byes are odd. For 11 teams (5 byes, an odd number): Upper Half = (5 − 1)/2 = 2 byes, Lower Half = (5 + 1)/2 = 3 byes.

The Correct Order of Allotment …