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?
- (a) 151
- (b) 150
- (c) 149 ✓ UPSC's answer
- (d) 148
Why the answer is (c)
• In a single-elimination tournament, every match results in exactly one player being eliminated.
• To determine the winner from 150 entrants, 149 players must be eliminated.
• Since each match eliminates exactly one player, the total number of matches required is equal to the number of players eliminated.
• Therefore, 149 matches are played to reduce the field from 150 to 1.
• This logic holds regardless of the specific bracket structure, as long as it is single-elimination with no ties.
Why the other options are wrong
- (a) 151
- 151 matches would imply 151 eliminations, which is impossible with only 150 entrants.
- (b) 150
- 150 matches would imply 150 eliminations, leaving no winner, which contradicts the tournament format.
- (d) 148
- 148 matches would eliminate only 148 players, leaving 2 players remaining instead of a single winner.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2022, held on 5 June 2022. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.