In a tournament of Chess having 150 entrants, a player is eliminated whenever he loses a match. It is given that no match results in a tie/draw. How many matches are played in the entire tournament?
Correct Answer :
149
Solution :
The correct option is 149.
To understand why this is correct, we can analyze the structure of a single-elimination tournament.
In this tournament, every match played has exactly one winner and one loser, as it is given that no match can result in a tie or a draw. Consequently, each match eliminates exactly one player from the tournament.
Let the initial number of entrants be represented by:
To determine the single winner (champion) of the tournament, all other players must be eliminated. Therefore, the total number of players that must be eliminated is:
Substituting the given number of entrants into the expression:
Since exactly one player is eliminated per match, the total number of matches played must equal the total number of eliminations required. Thus, the tournament requires exactly 149 matches to be played.
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