8 teams play against each other twice a season how many games are played

Question

 this question is so confusing i am having the hardest time with it

Answer 1

suppose the teams are...

A, B, C, D, E, F, G, H

and they play each other only once...

A plays B,C,D,E,F,G,H for a total of 7 games

B plays C,D,E,F,G,H for a total of 6 games (A already played B)

C plays D,E,F,G,H for a total of 5 games (C already played A and B)

D plays 4 games

E plays 3 games

F plays 2 games

G plays 1 game

H (everybody played H)

7+6+5+4+3+2+1=28 games played if each team plays every other team just once

but they play each other twice so 2*28=56 games played altogether

 

there is a pattern

if there are 3 teams A,B,C

A plays B twice, A plays C twice, and B plays C twice for a total of 6 games

3 teams times 2=6 games

4 teams A,B,C,D

A plays B twice, A plays C twice, A plays D twice, B plays C twice, B plays D twice, C plays D twice for a total of 12 games

4 teams times 3=12 games

5 teams, 5*4=20 games

6 teams, 6*5=30 games

7 teams, 7*6=42 games

8 teams, 8*7=56 games where each team plays every other team twice