Question 401605: 32 basketball teams went to a single elimination tournament. How many games were played at the tournament?
I don't really know how to figure this one out. If you do decide to help me, can you please show me how you did it? Many tutors just tell me the answer. I would like to know the steps for future reference. Thank you! :)
Found 2 solutions by robertb, jim_thompson5910:
Answer by robertb(5830)   (Show Source):
Answer by jim_thompson5910(35256)  (Show Source):
You can put this solution on YOUR website! The first answer is correct if there's only one actual game and you're trying to figure out how many ways to pair up two teams out of 32 (to play this only game).
However, in this case, it's much simpler.
Since there are 32 teams, and each team is playing someone else, there are  such pairings. Out of each pair, only one team will move on.
So after the first round, there are 16 teams left.
Those 16 teams pair up to have  pairings. So after the 2nd round, 8 teams remain. See the pattern?
So we go from 32, to 16, then to 8. Now divide 8 in 2 to get 4 and divide 4 in half to get 2. Finally, we have 2 teams that compete for the finals. If you cut 2 in half, you'll get 1, which will be the tournament champion.
So we have 16 (first round), 8 (second round), 4 (third round), 2 (fourth round) games and then 1 final game
Note: Count the pairings (NOT the actual teams). Draw a chart or a picture if you need to.
Note: the "fourth" round is probably more commonly known as the "semifinals". Also, the "third" round may be referred to as the "conference semifinals" or "quarterfinals"
So add up all of these games to get: 16 + 8 + 4 + 2 + 1 = 31
So this means that there are 31 games played total.
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