Question

139 persons have signed up for an elimination tournament. All players are to be paired up for the first round, but because 139 is an odd number one player gets a bye, which promotes him to the second round, without actually playing in the first round. The pairing continues on the next round, with a bye to any player left over. If the schedule is planned so that a minimum number of matches is required to determine the champion, the number of matches which must be played is

A.
136
B.
137
C.
138
D.
139

Answer

C

Explanation

In any elimination tournament with $N$ participants, every match eliminates exactly 1 player. To determine 1 champion from 139 players, $139 - 1 = 138$ players must be eliminated. Hence, exactly 138 matches must be played.

Accepted Answer

C. In any elimination tournament with $N$ participants, every match eliminates exactly 1 player. To determine 1 champion from 139 players, $139 - 1 = 138$ players must be eliminated. Hence, exactly 138 matches must be played.

Elimination Tournament Matches

Explanation

Practise this under exam conditions