a tournament question with any team number and all team positions?

Question

If there is any number of teams in a tournament, what is the minimum number of matches to know the positions of all teams?

For example:

4 teams (ABCD)

A vs B = A wins
C vs D = C wins
A vs C = A wins

A is number 1
B is number 2

B vs D = B wins

B is number 3
D is number 4

(4 matches)

What if there are 1024 teams in the tournament? How did you calculate it?

Answer 1

for N teams where N = 2^n, and n is an integer, your primary bracket alone needs
1 + 2 + 4 + 8 + 16 . ....2^(n-1) = N - 1games.
The secondary bracket requires N/2 -1 games.
The tertiary bracket requires N/4 - 1 games.
thus
2 teams require 2 - 1 game
4 teams require 4 - 1 + 2 - 1 = 4 games
8 teams require 8 - 1 + 4 - 1 + 2 - 1 = 11 games
16 teams require 16 - 1 + 8 - 1 + 4 - 1 + 2 - 1 = 26 games
32 teams require 32 - 1 + 16 - 1 + 8 - 1 + 4 - 1 + 2 - 1 = 57 games
Rewriting, we have
2^1 teams require 2 - 1 game
2^2 teams require 4 + 2 - 2 = 4 games
2^3 teams require 8 + 4 + 2 - 3 = 11 games
2^4 teams require 16 + 8 + 4 + 2 - 4 = 26 games
2^5 teams require 32 + 16 + 8 + 4 + 2 - 5 = 57 games
2^n teams require 2(2^n - 1) - n games
1,024 = 2^10 teams requiring
2(1023) - 10 = 2,036 games

Note that this bracketing for 2^n teams provides only n definitive rankings. The remainder are ambiguous.

As you may already know, numbers other than integer powers of 2 are devilishly difficult to bracket. This is perhaps one reason why tournaments rarely bracket even to the tertiary level.

Answer 2

Stupid question (in which you have B both at number 2 and number 3) and stupid answers.


There is no minimum amount of games. Doesn't matter how many games you play, there is always a possibility for a tie (same amount of wins and losses) between any 2 (or more) teams.

Answer 3

Wow .. umm iwould suggest a NCAA March Madenss stlye bracket and exspanding it.. there are 64 teams in the NCAA bracket so do 16 of them

Answer 4

omg i hope you aint organising a tournament with that many teams...maybe you should get a computer program to help you