Expert: Steve Holleran - 11/28/2007

Question
Can you help me to solve this problem without using factorial?
At a basketball tournament involving 8 teams,each team played 4 games with each of the other team. How many games were played at the tournament?
                                   Thanks a lot,
                                             Angela

Answer
Hi Angela,

I would try something like this:

Make a diagram and use 8 letters for the teams:

                 a      b

          h                    c

                              
          g                    d

                   f     e

Now on your diagram, draw a line to each letter to represent a game. start at a, and draw lines to b,c,d,e,f,g,h.  That's 7 games.  Then go to b, do the same, but don't count the line already linking it to a.   There should be 6 of these.  Keep going, and for c you'll get 5, d= 4, and so on.  

That's a total of 28 games.  Then multiply by 4 to get 112.

Steve