Start here · the first lesson of Knockout rounds
Knockout rounds
Games and Tournaments · for IPMAT Indore, IPMAT Rohtak and JIPMAT
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The idea
Losers leave; winners advance. Matches = players - 1, rounds = log2 N. Seeding rules decide who can meet whom, and an upset is a win by the worse seed.
Textbook vs exam method
Textbook method
- Number of rounds and players left after each round: N / 2^r.
- Write the pairing rule (best v worst) for the round you need.
- For "possible opponent" questions, trace back to the first-round matches.
- For upset counts, count the opponents better than the winner.
Exam method
- Halving list. 128, 64, 32, 16, 8, 4, 2, 1 gives every count question in seconds.
- No-upset rule. seed 45 in a 128-player draw is out in the round where it is in the lower half of those left.
- Upset minimum. a seed s meets only worse seeds until the field has fewer players than s; every later win is an upset.