A set of soccer games is to be organized in a round robin (e.g. every team plays a match against each other one time). If 45 games are played, how many teams participated?
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If 10 teams participated, then the first team plays games against the other 9 teams. The second team has already played against the first team so it has to play games against only the other 8. In this way the second-last team has to play against only one team, and the last team has already played against the others. Therefore the total number of games is 9 + 8 + …….. + 2 + 1 = 45.