SOLUTION: I am a seventh grade student who has to do a problem of the week each week. this is the one for this week. Seventy-Eight players entered a single elimination tennis tournamen

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Question 22009: I am a seventh grade student who has to do a problem of the week each week. this is the one for this week.
Seventy-Eight players entered a single elimination tennis tournament. How many matches were played to determine the over all champ.
I have tried to figure this out. I started by dividing 78 by 2 and came up with 39 original matches. My problem is that if I divide that in 1/2 again to come up with the next set of matches, (19 matches) then I have one person left over who does he play? I thought about having him play a person from a future round but that person will have won more games so it wouldn't be fair. Please help. I just don't understand what to do.
Thank You
K.I.
Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website!
YOU ARE PROCEEDING ON RIGHT LINES GO AHEAD...
OFCOURSE THERE IS A FUNDAMENTAL ASSUMPTION MADE TO START WITH THAT IS ELIMINATION IS BY KNOCK-OUT...NOT ON LEAGUE BASIS IN WHICH CASE EACH PLAYER WILL PLAY WITH ALL OTHERS TO MAKE A LONG SERIES OF
3003 MATCHES WHICH YOU WILL KNOW IN HIGHER CLASS..
.NOW FOR THE PRESENT TAKE KNOCK-OUT BASIS AS YOU HAVE TAKEN GIVING A BYE TO ODD PLAYER AND INDUCTING HIM INTO THE NEXT ROUND.IT WILL RESULT IN SOME UNEVEN MATCHES PLAYED BY DIFFERENT PLAYERS BUT THAT GOES BY LUCK OF THE DRAW...
SO WE HAVE
I ROUND =78/2=39 MATCHES
II ROUND =38/2=19 MATCHES WITH 1 PLAYER GIVEN BYE BY LOTS
III ROUND =(19+1 BYE)/2=10....LIKE THAT YOU CAN PROCEED...BUT YOU ARE RIGHT IN INFERING IT ENTAILS UNEVENPLAY OFFS...SO ATLEAST AFTER SOME STAGE A LEAGUE BASIS WOULD BE GOOD SAY FOR THE LAST 5 WHEN WE NEED 10 MATCHES FOR 5 PEOPLE PLAYING LEAGUE