Question

How many byes will be given if there are 17 teams in a knockout tournament?

• A. 1
• B. 8
• C. 15
• D. 12

Hint:

Formula: Byes = Next power of 2 − Number of teams.

Answer 1

The Correct Option is C

Concept: In a knockout tournament, the total number of teams must be a power of 2 (like 2, 4, 8, 16, 32). If the number of teams is not a power of 2, byes are given to adjust it to the next power of 2.
Step 1: Find Next Power of 2 Number of teams = 17 Nearest power of 2 greater than 17: \[ 2^5 = 32 \] Step 2: Calculate Byes \[ \text{Byes} = 32 - 17 = 15 \] \[ \boxed{15} \]

Answer 2

A single-elimination (knockout) draw is really a bracket with a fixed number of "slots," and that number of slots always has to be a power of 2, because each round exactly halves the field. To fit 17 teams into such a bracket, we need to find the bracket size and see how many empty slots (byes) are left over.

1. 1: This would mean only one slot in the entire draw is left empty, which is far too small a bracket to accommodate 17 real teams properly across rounds; it does not match the structure of a valid knockout draw.
2. 8: A bracket with 8 empty slots would mean a total bracket size of 17 + 8 = 25 slots, but 25 is not a power of 2, so such a bracket cannot actually be built as a proper knockout draw.
3. 15: A bracket with 15 empty slots gives a total size of 17 + 15 = 32 slots, and 32 is exactly \( 2^{5} \), a valid power of 2. This means the draw sheet is built for 32 positions; 17 of them hold real teams and the remaining 15 positions are left blank. Whichever team is paired against a blank slot in the first round automatically advances without playing, which is what a bye is.
4. 12: Here, 17 + 12 = 29 slots, and 29 is not a power of 2 either, so a bracket of this size is not structurally possible for a knockout format.

Since a knockout bracket can only be built at sizes that are powers of 2, and 32 is the smallest such size that can hold 17 teams, the leftover, unfilled slots, and therefore the byes, must number 15.

Therefore, the correct answer is 15.