Federer won again! What an inspirational game!

In the spirit of tennis, here's a question for you:

One thousand and twenty four tennis players compete in a singles competition (one player play against another - loser cannot play any further, winner stays in the game and play another winner, etc.). Assuming all players play, how many games are there until there is a champion?

## Sunday, January 28, 2007

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## 2 comments:

1023.

Each game eliminates one player, and all but one player must be eliminated for there to be a champion, therefore there must be 1024 - 1 = 1023 games.

Notice that 1028=2^10, and in the first round there are 512=2^9 games. In general, if there are 2^n players in each round there will be 2^(n-1) matches played in that round.

So the number of games is equal to:

SUM_{i=0)^{i=9} 2^n.

Now notice that 2^9=512, 2^8=512/2 etc... So that each time you add on a "decresing power" you're halving the distance to 1024. You finish by adding 1 on, which is therefore the 1023rd game.

There are 1023 games.

TSR user name: JohnSPals

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