How to solve this question? topic is on Permutations and combinations!

Question

139 persons have signed 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 1

1st round: 69 matches, 69 winners +1 bye

2nd round: 35 matches, 35 winners

3rd round: 17 matches, 17 winners + 1 bye

4th round: 9 matches, 9 winners

5th round: 4  matches, 2 winners + 1 bye

6th round: 1 match, 1 winner + 1bye

7th round: 1 match, Champion!