sports tournament draw formula

Question

Suppose we have a sport tournament with direct elimination. The original number of players is a perfect power of 2, say n. Each player is attributed a draw position, between 1 and n. The tournament's first round is organized in the following way:

match 1: 1 vs 2
match 2: 3 vs 4
...
match n/2: n-1 vs n

Matches are numbered in order from top to bottom for each round.

Given a particular match, how can we express the range each player draw position can be from the round number and the match number ?

e.g:

Round 2, match 1:
P1 is in [1,2]
P2 is in [3,4]

Round x, match m: P1 is in ? P2 is in ?

Thank you

if you -1 me please say why thank you. – Etienne Dec 07 '15 at 00:07 — Etienne, Dec 07 '15 at 00:07

score 1 · Accepted Answer · answered Dec 07 '15 at 00:53

1

Round X, match m:

P1 is in $[(m-1)2^X+1 , (m-1)2^X +2^{X-1}] $

P2 is in $[(m-1)2^X +2^{X-1}+1 , m 2^X] $

answered Dec 07 '15 at 00:53

WW1

10,497

works wonderfully thanks a lot. – Etienne Dec 07 '15 at 03:32

sports tournament draw formula

1 Answers1