Correct Option (3)
In a single-elimination tournament, the fundamental principle is that each match played results in the elimination of one player. The tournament concludes when only one player remains undefeated, who is then declared the winner. To achieve a single winner from an initial pool of participants, all other participants must be eliminated.
- Initial number of entrants = 150.
- To determine a single winner, 149 players must be eliminated.
- Since each match eliminates exactly one player (as no ties or draws are permitted), the total number of matches played directly corresponds to the number of players eliminated.
- Therefore, 149 matches are required to eliminate 149 players and determine one champion.
Incorrect Options:
The other options are incorrect as they do not align with the mechanics of a single-elimination tournament where each match produces one loser and one winner until a single champion is identified.
- Option 1 (151): This number of matches would imply more eliminations than necessary to determine a single winner from 150 players, or suggests a different tournament structure.
- Option 2 (150): If 150 matches were played, it would mean all 150 players were eliminated, leaving no winner, which contradicts the objective of a tournament.
- Option 4 (148): This number of matches would result in only 148 players being eliminated, leaving two or more players undefeated, thus failing to determine a single champion.
