Answer:
156 games
Step-by-step explanation:
You want to know the total number of games when each of 13 teams plays every other team exactly twice.
Each of the 13 teams will meet 12 others, for a total of 13×12 = 156 meetings.
This total counts the time team 1 meets team 2, and also the time team 2 meets team 1. In other words, this is exactly the game count we're looking for.
156 games will be played.
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Alternate solution
Team 1 will meet teams 2 through 13, for a total of 12 games. Team 2 has already met team 1, so will need to meet teams 3 through 12 for a total of 11 games. When we count all the games for one meeting between teams, we find the count to be 12 +11 +10 +9 +... +1 = (12)(13)/2 = 78.
If the teams are to meet twice, then 2 times this number of games will be played: 2(78) = 156.
The sum of integers 1 .. n is (n)(n+1)/2.
