Tennis Tournament

Strategies and Hints

There are 4 byes. For our example there were 17 teams. To determine the number of byes you would subtract 17 from the lowest power of 2 greater than 17. This is 32, since 2 to the fifth is 32 and 2 to the sixth is 16. This leaves 15. Next, you express 15 in binary notation which is 1111. The number of byes is equal to the number of 1's in this expression, in this case 4.




Extensions:

  1. To determine the number of byes for any number of teams, you need to start by subtracting the number of teams from the lowest power of 2 greater than that number. You then need to express the answer in base 2. The number of byes is the number of 1's in this expression.

  2. The number of games played is always (n - 1) since each game eliminates one team.