document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #698360 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "In each round, exactly one half of participants is eliminated from the tournament.\r\n" );
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document.write( "Therefore, the sequence of the numbers of survived participants and the number of matches in each round is this:\r\n" );
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document.write( " round     N of particicipants      N of matches\r\n" );
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document.write( "   1        512 =                  = \r\n" );
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document.write( "   2                                     \r\n" );
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document.write( "   3                                     \r\n" );
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document.write( "   4                                     \r\n" );
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document.write( "   5                                     \r\n" );
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document.write( "   6                                     \r\n" );
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document.write( "   7                                     \r\n" );
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document.write( "   8                                      = 2   (semifinal)\r\n" );
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document.write( "   9               = 2                   1         (final)\r\n" );
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document.write( "Total (sum)                                 = 511 matches.\r\n" );
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