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wildguy

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Sep 29, 2014
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Hi Everyone,

NOt sure how to answer this questions any thoughts?

There are k teams in a high school football conference. During regular in season games, each team will play against each of the other teams exactly once. How many total regular in season games will there be in the football conference?

Thank you for your input:D
 
wildguy said:
NOt sure how to answer this questions any thoughts?

There are k teams in a high school football conference. During regular in season games, each team will play against each of the other teams exactly once. How many total regular in season games will there be in the football conference?
Click to expand...
How many games were played when there were two teams?

How many games were played when there were three teams?

How many games were played when there were four teams?

Continue until you see a pattern. Develop a formula for that pattern. (Depending upon the rigour of your class, you may need then to prove the pattern by induction or some other method.)

Have fun! ;)
 
wildguy said:
I'm looking for an equation
Click to expand...

Start with teams 1. They can play each of the other k-1 teams.
For team 2, they have already played team 1 so they can play the other k-2 teams
Team 3 have played teams 1 & 2 so they can play the other k-3 teams
....

Add them up.
 
Ishuda said:
Start with teams 1. They can play each of the other k-1 teams.
For team 2, they have already played team 1 so they can play the other k-2 teams
Team 3 have played teams 1 & 2 so they can play the other k-3 teams
....Add them up.
Click to expand...
stapel said:
Continue until you see a pattern. Develop a formula for that pattern. (Depending upon the rigour of your class, you may need then to prove the pattern by induction or some other method.
Click to expand...

Because you were not given the chance to find the answer on your own, you should see a correct solution.

The answer is exactly the same as "How many line segments are determined by \(\displaystyle k\) points:
\(\displaystyle \dbinom{k}{2}=\dfrac{k(k-1)}{2}\)".
 
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