two part analysis question

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two part analysis question

by datonman » Sun Nov 08, 2015 5:22 pm
A city is hosting a table tennis tournament for its residents. Each team has exactly two players, and each team is on exactly one team. In each round, each team plays exactly one other team and either wins or loses. The winning team advances to the next round and the losing team is eliminated. No team or player drops out except by losing a game. The tournament is in progress, and exactly 512 players participated in the first round.

From the available options, select a number of tournament rounds and a number of teams such that after the specified number of rounds there will be the specified number of teams remaining in the tournament. Make only two selections, one in each column.
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by [email protected] » Mon Nov 09, 2015 7:08 am
datonman wrote:A city is hosting a table tennis tournament for its residents. Each team has exactly two players, and each team is on exactly one team. In each round, each team plays exactly one other team and either wins or loses. The winning team advances to the next round and the losing team is eliminated. No team or player drops out except by losing a game. The tournament is in progress, and exactly 512 players participated in the first round.

From the available options, select a number of tournament rounds and a number of teams such that after the specified number of rounds there will be the specified number of teams remaining in the tournament. Make only two selections, one in each column.
We know that if there are two players per team, and there are 512 players, there are 512/2 = 256 teams. After each round, half the teams are eliminated. So after one round, there will be 128 teams left. After two rounds, there will be 64 teams left. After 3 ---> 32 left. After 4 ---> 16 left. After 5 ---> 8 left. After 6 ---> 4 left. After 7 ----> 2 left. After 8 ---> 1 left, and this team won the tournament.

Of the above options, the only possibility that will work is that after 4 rounds, there will be 16 teams remaining.
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