Start with team 1, they will play 9 other teams, so there are 9 games.

Team 2 will play 9 teams as well, but you already counted team 1, so that is another 8 unique games.

Team 3 will play 9 teams too, but you already counted teams 1 and 2, so that is another 7 unique games.

Continue this process and you will have 9+8+7+6+5+4+3+2+1=45.

team A will play:

B C D E F G H I J

team B will play the same teams minus A because they already played them:

C D E F G H I J

team C will play all minus A and B

D E F G H I J

team D will play all minus A B and C

E F G H I J

team E will play all minus A B C and D

F G H I J

team F will play all minus A-E

G H I J

team G will play all minus A-F

H I J

team H will play all minus A-G

I J

team I will play all minus A-H

J

now count all of those letters underneath the “team _ will play all minus _-_” I think thats 45, but you can count for yourself.