A league of 20 teams is playing a "round-robin" style tournament,

Question

A league of 20 teams is playing a "round-robin" style tournament, where each team plays every other team exactly once. How many games total need to be played?

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Justify your answer using a graph model—say what the vertices and edges of your graph represent, and what (if any) theorems you use. (Upload your file below.)

Answer 1

Team 1 plays 19 games and leaves

Team 2 plays 18 games and leaves

Team 3 plays 17 games and leaves

Team 4 plays 16 games and leaves

And so on.

Can you answer?

Answer 2

Mark's method is fine. sum of all integers from 19 down through 1 is 19(20)/2 = 190.

 

By experimenting with a small (even) # of teams, say 4, (ABCD), you get the following games: AB AC AD;

BC BD; CD. That's 6 games. This is actually 4C2, a combination calculation, that is equal to 6.  

By extension, 20C2 is the answer, which is exactly 190.