Please solve this

Question

Mr. Knight is the organizer of the Canadian Chess Tournament. 765 contestants sign up. The tournament is designed so the winner of each round advances and the loser is eliminated. Since there is an odd number of participants, the initial pairing leaves one player out who automatically advances to round two. How many chess games must be scheduled to determine a winner?

Answer 1

Top ranked player gets 2 BYES and starts in the third round.

 

764 / 2 = 382

 

382/2 = 191 

 

192/2 = 96

 

96/2 =  48

 

48/2 = 24

 

24/2 = 12

 

12/2  = 6

 

6/2 = 3   <--- top remaining seed gets a bye

 

2/2 = 1

 

2/2 = 1

 

764

 

 

In general,  If there are N participants in the single elimination tournament,

it can be proven by induction that there are N-1 games played.