35 teams enter a basketball competition. Assuming there are no replys or drawn games. How many games are played until there is a winner?

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- Jul 7th 2007, 10:22 AM #1

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- Jul 7th 2007, 10:27 AM #2

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- Jul 7th 2007, 10:38 AM #3

- Jul 8th 2007, 04:01 AM #4

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- Jul 8th 2007, 04:07 AM #5

- Jul 8th 2007, 06:13 AM #6

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- Jul 8th 2007, 06:24 AM #7
Perhaps the question is supposed to be more like 'how many games does the winning team play"?

In which case, since 35 is odd one team at the beginning moves on without playing. (I forget what the correct term for that is. Is it a "bye" or something?) So the first round eliminates $\displaystyle \frac{36}{2} - 1 = 17$ teams, leaving 18.

The second round eliminates 9 teams, leaving 9 teams.

The third round includes that "bye" thing (or whatever), so $\displaystyle \frac{10}{5} - 1 = 4$ teams are eliminated, leaving 6 teams.

The fourth round eliminates 3 teams, leaving 3 teams.

The fifth round includes a bye, so $\displaystyle \frac{4}{2} - 1 = 1$ team is eliminated leaving 2 teams.

The sixth round is the final and eliminates 1 team.

So the winning team plays 6 games.

-Dan

- Jul 8th 2007, 06:26 AM #8

- Jul 8th 2007, 06:35 AM #9

- Jul 8th 2007, 09:52 AM #10

- Jul 8th 2007, 01:48 PM #11
Hmmm...

I believe that a bye does technically count as a game, but you are right... they really didn't play did they? Then the answer to my question must vary between 3 and 6 games.

Since this isn't a definite answer I suppose that means my thought is pointless. Ah well!

-Dan