Some game shows sponsor tournaments where in each game, three individuals play against each other, yielding one
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Some game shows sponsor tournaments where in each game, three individuals play against each other, yielding one winner and two losers. The winners of three such games then play each other, until the final game of three players produces a tournament winner. Suppose 81 people begin such a tournament.
(a) Write a geometric sequence whose sum determines the number of games that must be played to determine the tournament champion.
(b) How many games must be played to produce the champion?
(c) Generalize parts (a) and (b) to a tournament where 3n players are initially present.
(d) Further generalize parts (a) and (b) to a tournament where tn players are initially present.
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a In round one there are 81 players playing in 813 27 games that produce 27 winners to play in round ...View the full answer
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