There are 10 teams. Each team plays against each of the other teams once. This means every team plays the other 9 teams once each, which is 9 games for each team.

Example : team 1 plays against team 2,3,4,5,6,7,8,9,10 once.
Number of games = 9

Example : team 5 plays against team
2,3,4,6,7,8,9,10 once.
Number of games = 9


By this logic, Number of games = 9 games per team x 10 teams
= 90 games.

However, realise that when two teams play against each other, it is only counted as 1 game. But if we multiply 9 x 10, we have doubled counted.

For example, team 1 vs team 2 is considered one game. But above we have considered it as one game per team.

So we must divide by 2.

90 games ÷ 2 = 45 games

Method 2

team 1 plays against 2,3,4,5,6,7,8,9,10 once first.

Number of games = 9

Now, team 2 already played with team 1. So team 2 plays with 3,4,5,6,7,8,9,10 once

Number of games = 8

team 3 played with team 1 and 2 already.
So team 3 plays with 4,5,6,7,8,9,10 once

Number of games = 7


So on and so forth. Eventually, when it's team 9's turn, team 9 plays with team 10 once as they already played with the first 8 teams before.

Number of games = 1

Now, team 10 doesn't have to play anymore as it has already played with teams 1-9 once each.

Total number of games
= 9+8+7+6+5+4+3+2+1
= 45

Thanks much!

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