In a 10-team Ieague, each team plays every other team exactly twice. Find the total number of games played in the league.?

Answer 1

There are 10 teams, so any given team will play all of the other 9 teams, resulting in 9 games for each of the 10 teams.

Multiply the 10 teams by the 9 games each team times 2 times will play to yield 180 games.

180 games includes duplicates (i.e., double-counting). In the counting of 180 games, we included the games team 1 played against teams 2 to 10. However, when we counted the number of games played by team 2, and likewise by teams 3 to 10, we also counted the games that these teams played against team 1.

In other words, you cannot count as a unique game both Team 1 vs. Team 2 and Team 2 vs. Team 1. Based upon the question ("how many games are played in total"), we must find the number of unique games.

Based upon this double-counting, 180 games is twice the number of games actually played. If we include only half the games we counted (including games such as team 1 vs team 2 while eliminating non-unique games such as team 2 vs team 1), we end up with a total count of 90 games (=180/2).

Answer 2

This is for 8th grade, good luck!

Answer 3

90 games