97 baseball teams participate in an annual state tournament. The champion is chosen for this tournament by the usual elimination scheme. That is, the 97 teams are divided into pairs, and the two teams of each pair play against each other. The loser of each pair is eliminated, and the remaining teams are paired up again, etc. How many games must be played to determine a champion?

general knowledge math & puzzles

  1. 95

  2. 96

  3. 97

  4. 98

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Correct Option: B

AI Explanation

To determine the number of games required to determine a champion in the given scenario, we need to consider the elimination scheme.

In each round, half of the teams are eliminated. Since there are 97 teams initially, we can represent this as a series of elimination rounds:

Round 1: 97 teams Round 2: 48 teams Round 3: 24 teams Round 4: 12 teams Round 5: 6 teams Round 6: 3 teams Round 7: 2 teams (final) Round 8: 1 team (champion)

To find the total number of games, we can sum up the number of games played in each round. In each round, the number of games played is half the number of teams remaining.

In Round 1, there are 97 teams, so 97/2 = 48.5 games are played. However, since we cannot have half a game, we need to round up to the nearest whole number. Therefore, in Round 1, 49 games are played.

In Round 2, there are 48 teams, so 48/2 = 24 games are played.

In Round 3, there are 24 teams, so 24/2 = 12 games are played.

In Round 4, there are 12 teams, so 12/2 = 6 games are played.

In Round 5, there are 6 teams, so 6/2 = 3 games are played.

In Round 6, there are 3 teams, so 3/2 = 1.5 games are played. Rounding up to the nearest whole number, 2 games are played.

Therefore, the total number of games played to determine a champion is 49 + 24 + 12 + 6 + 3 + 2 = 96.

The correct answer is B) 96.

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