Help! Math Problem of the Week!

[Tung]

The intramural tennis club in South Bend, Indiana wants to schedule a single elmination touranment to name their city's champion double teams. There will be 17 teams in the tournament. If each doubles team must either play or be granted a "bye" in each round, how many games and byes must be scheduled in order to produce one championship? How many games and byes must be scheduled if Indanapolis had 72 teams?

Questions:
1) If the teams just kept playing until all were elimated and no "byes" were granted, how many games would be played?
2) How does this fact that teams must play or have a "bye" at each level of elimination affect the total number of games?


please help in any way you can. my sister had this for her problem of the week, and i've asked all around but no one knows how to do it.

 

[IscareCuzICare]

<< If each doubles team must either play or be granted a "bye" in each round, how many games and byes must be scheduled in order to produce one championship? >>


16 games and 4 "bye"'s.



<< How many games and byes must be scheduled if Indanapolis had 72 teams? >>


36+18+9+4(1 "bye")+2(1 "bye")+1(1 "bye")=70+3"bye"s

1)

<< If the teams just kept playing until all were elimated and no "byes" were granted, how many games would be played? >>


If no "bye" were granted, there would be 17!/15!/2!*2= 272 games *m'thinks*
2)

<< How does this fact that teams must play or have a "bye" at each level of elimination affect the total number of games? >>


*No comment *

 

[mss242]

<< 1) If the teams just kept playing until all were elimated and no "byes" were granted, how many games would be played? >>



16 and 71. one round gives one loss and each team gets one loss except for the final winning undefeated team.



<< 2) How does this fact that teams must play or have a "bye" at each level of elimination affect the total number of games? >>



well, if it is a rounded tournament (finals, semi's quarters, etc. ) in the 17 team match there would first be partial double octas with only one round. 17 would play 16. The winner of that would then enter as the 16th seed to octa finals. After that point there would be 8+4+2+1=15 matches. add one for the double-octa round and the 15 byes awarded in that round and the total comes to 31. Apply a similar method to the case of 72 teams.

I hope that helps

 

[Tung]

thank you IscareCuzICare and mss242. your responses really help!!!