DAY 46

Comment

You could list all the games, but there are more elegant ways (though it can help to start listing the games).
Another approach is to start with one team:
How many home games does it play?
What else do we need to know?

Answer

90 games are played altogether.

Readers' methods

Erich von B, Seewiesen, Munich:
Team A plays 9 teams twice, which is 18 games.
In addition, team B plays 8 other teams twice, which is 16 games.
In addition, team C plays 7 other teams twice, which is 14 games.
And so on.
So altogether there are 18 + 16 + 14 + 12 + 10 + 8 + 6 + 4 + 2 games, which is 90 games.

Ben B, Harrow HA2:
Each team plays a home match against the other nine,
therefore 10 x 9 matches = 90 matches in a season.

Senthil Kumar, Hyderabad, India:
If n is the domain to choose a set of r, then combination C can be given as
nCr = n!/r!(n-r)!.
Applying the same to this problem, we get
10C2 = 10!/2!.8! = 10x9/2 = 45.
Since the teams meet twice, the 10 teams play 90 matches.