How many matches does a knockout tournament need?
A 127-player single-elimination tournament needs a schedule even though its opening bracket is not a neat power of two. Can you work out the number of matches without drawing every round? Look for something each completed match changes, then test whether byes affect the count.
Questions you could explore
- What must happen to every entrant except the champion in a single-elimination tournament?
- Why do byes not change the total number of eliminations needed?
- How would a third-place playoff or double-elimination format change the assumptions?
Start reading
- NRICH, University of CambridgeTournament Scheduling
NRICH introduces single-elimination formats and byes; counting eliminations supplies the short argument for the stated model.
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