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Math Help - Tournament Rules

  1. #1
    Newbie Spartan 68868's Avatar
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    Tournament Rules

    In a certain tournament a player mist be defeated three times to be eliminated. If 512 contestants enter the tournament what is the greatest number of games that could be played?
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  2. #2
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    Say you only have 3 players.
    The maximum number is: 2+2+2+1+1

    If 4 then: 2+2+2+2+1+1+1

    If 5 then: 2+2+2+2+2+1+1+1+1

    We see that general formula is, if n>=3 players then:
    (2+2+...+2)+(1+1+...1)

    Where 2 appears n times and 1 appears n-1 times.
    Thus,
    2n+1(n-1) = 3n - 1

    Thus, if you have 512 that means,
    3(512)-1
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Spartan 68868 View Post
    In a certain tournament a player mist be defeated three times to be eliminated. If 512 contestants enter the tournament what is the greatest number of games that could be played?
    Assume that in a game one player wins and the other loses, that is no draws.

    At the end of the tournament 511 players have each lost 3 games, and the
    winner may have lost 0, 1 or 2 games. As each, and every game had a loser
    then there were 3*511, 3*511+1 or 3*511+2 games, the largest of these is
    3*511+2=3*512-1.

    RonL
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