SOLUTION: The Scrabble tournament is designed such that the losers of each round are eliminated from the next round. The winners continue to play until a final match determines the champion.

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Question 1084273: The Scrabble tournament is designed such that the losers of each round are eliminated from the next round. The winners continue to play until a final match determines the champion. If there are 512 entries in the tournament, what is the total number of matches that will be played in this tournament?
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
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In each round, exactly one half of participants is eliminated from the tournament.


Therefore, the sequence of the numbers of survived participants and the number of matches in each round is this:


 round     N of particicipants      N of matches

   1        512 = 2%5E9                512%2F2 = 2%5E8

   2              2%5E8                       2%5E7

   3              2%5E7                       2%5E6

   4              2%5E6                       2%5E5

   5              2%5E5                       2%5E4

   6              2%5E4                       2%5E3

   7              2%5E3                       2%5E2

   8              2%5E2                       2%5E1 = 2   (semifinal)

   9              2%5E1 = 2                   1         (final)
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Total (sum)                                2%5E9-1 = 511 matches.