# Its a knockout

wolfgang59
Posers and Puzzles 10 Jul '07 20:46
1. wolfgang59
Mr. Wolf
10 Jul '07 20:46
In a knockout competition (Wimbledon?) where there can be no draws, N teams enter. In the first round there are 'R1' matches and 'b' byes such that 'R1' - n is a power of 2. Thus the remaining rounds halve the participants until there is a winner in final.

eg N=10, then R1=2 and b=6 leaving 8 teams after first round. Then 4 teams are after 2nd, then 2 after 3rd then 1 winner.

Question: What is the total number of matches before there is a champion?
2. 10 Jul '07 20:49
Originally posted by wolfgang59
In a knockout competition (Wimbledon?) where there can be no draws, N teams enter. In the first round there are 'R1' matches and 'b' byes such that 'R1' - n is a power of 2. Thus the remaining rounds halve the participants until there is a winner in final.

eg N=10, then R1=2 and b=6 leaving 8 teams after first round. Then 4 teams are after 2nd, then ...[text shortened]... n 1 winner.

Question: What is the total number of matches before there is a champion?
Hint: Everyone loses once, except the winner of the competition, right?
3. wolfgang59
Mr. Wolf
10 Jul '07 20:52
Fabian - you are no fun!
4. 10 Jul '07 21:23
Originally posted by wolfgang59
In a knockout competition (Wimbledon?) where there can be no draws, N teams enter. In the first round there are 'R1' matches and 'b' byes such that 'R1' - n is a power of 2. Thus the remaining rounds halve the participants until there is a winner in final.

eg N=10, then R1=2 and b=6 leaving 8 teams after first round. Then 4 teams are after 2nd, then ...[text shortened]... n 1 winner.

Question: What is the total number of matches before there is a champion?
I'd suppose it's N - 1 because to find out a winner, everyone else must be eliminated, therefore, 1 match for each loss of every other team. 10 teams, 9 matches, 1 winner, 9 losers.
5. wolfgang59
Mr. Wolf
10 Jul '07 21:26
yes ... :-(
6. 11 Jul '07 07:02
Isn't there a match for the bronze winner too in Wimbledon...?
7. 11 Jul '07 10:37
Originally posted by FabianFnas
Isn't there a match for the bronze winner too in Wimbledon...?
Nope, there isn't.