How Many NCAA Games?

Probability Level 1

In the single-elimination NCAA Tournament, 64 teams compete in 6 bracketed rounds. How many games are there in total?

2 6 − 1 = 63 2^{6}-1 = 63 2 6 + 1 = 65 2^{6}+1 = 65 2 6 = 64 2^{6} = 64 2 6 − 1 = 32 2^{6 - 1} = 32

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Zandra Vinegar by Zandra Vinegar

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3 solutions

Zandra Vinegar Staff
Aug 14, 2015

64 teams participate in the tournament. Since it's single-elimination, each team but the winner of the tournament loses once. Therefore, there are 63 games.

In general, if 2 n 2^n teams are competing in a single-elimination tournament, there will be 2 n − 1 2^n-1 games.

29 Helpful 0 Interesting 7 Brilliant 0 Confused

Ma'am what does STAFF signify?It is present besides only a few person's name.Also thanx a lot for ur explanation.

Kaushik Chandra - 4 years, 8 months ago

Also, in general, if there are n teams in an elimination tournament, there are n-1 games. 64 - 1 = 63 games.

Siva Budaraju - 4 years, 4 months ago

Ok but why do I have to subtract 1

Connor Kolan - 1 year, 7 months ago

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Personally, I did it by substituting small numbers first and making conjectures. If there are 2 teams, how many games are there? If there are 4? If there are 8? By counting you can see they follow a rule 2^n-1

Kano Boom - 1 year, 7 months ago

64 teams there are: 2 at power 5 games first round,2 at power 4 games second round,2 at power 3 games third round,2 at power 2 games fourth round, 2 at power 1 games fifth round, 2 at power 0 games sixth round. The sum of this is 2 at power 6 minus one games .

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice - do you have a general rule for manipulating powers that proves this? Thanks. C.

Chris Crawford - 4 years, 9 months ago
Bostang Palaguna
Aug 17, 2020

the number of tournaments: 32 + 16 + 8 + . . . + 1 32 + 16 + 8 + ... + 1 .

by using geometric series, this is equivalent to 2 6 − 1 \boxed{2^6 -1}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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