Posers and Puzzles

Posers and Puzzles

  1. Standard memberwolfgang59
    Mr. Wolf
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    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. Joined
    11 Nov '05
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    43938
    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. Standard memberwolfgang59
    Mr. Wolf
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    10 Jul '07 20:52
    Fabian - you are no fun!
  4. Sigulda, Latvia
    Joined
    30 Aug '06
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    4048
    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. Standard memberwolfgang59
    Mr. Wolf
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    10 Jul '07 21:26
    yes ... :-(
  6. Joined
    11 Nov '05
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    43938
    11 Jul '07 07:02
    Isn't there a match for the bronze winner too in Wimbledon...?
  7. Joined
    24 Mar '05
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    44231
    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.
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