Answered

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In a baseball league consisting of 13 teams, each team plays each of the other teams twice. How many games will be
played?

Sagot :

sqdancefan

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.

Games

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.

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