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!

So, if the number of matches are added together, we get the minimum number of matches that need to be played which is 136

Answer 2

Answer:

The correct option is C. 138

Step-by-step explanation:

• 1st round :

Matches = 139 - 1 = 138/2 = 69 and 69 winners

Bye given = 1

• 2nd round :

Matches = 35 and 35 winners

• 3rd round :

Matches played = 17 and 17 winners

Bye given = 1

• 4th round :

Matches played = 9 and 9 winners

• 5th round :

Matches played = 4 and 4 winners

Bye given = 1

• 6th round :

Matches played = 2 and 2 winner

Bye given = 1

• 7th round :

Matches played = 1 and 1 winner

Bye given = 1

• 8th round :

Matches played = 1 and 1 winner or champion

So, Total number of matches to be played = 69 + 35 + 17 + 9 + 4 + 2 + 1 + 1

                                                                          = 138

Hence, The correct option is C. 138