How many games teams play in soccer tournament?

3/5/2010

This problem is very similar to 'handshakes' problem.

I had 2 groups of children. First group had 3 kids and the second had 4 kids. Each child represented a soccer team. All those teams are playing in soccer tournament. In first group there are 3 teams and in the second there are 4. Teams play against another 3 games. How many games played in each group?

To solve this I reminded children about 'handshake' problem. Each handshake represents a game.
Kids did handshakes and calculated total number of games. Kids in both groups calculated number of games correctly by just counting total number of handshakes among each other.

Then I asked them to step back. I reminded them how we could solve similar problems by applying arithmetic progression: 3 handshakes between 2 kids, 6 if add third kid, 9 when fourth kid is added. So we have 3+6+9=18.

After that I asked: What if we add 5th team? We would have 3+6+9+12=30.
I reminded them how we can calculate the sum of arithmetic progression. Add the first and the last numbers (3+12=15) and add the second and second from the last numbers(6+9=15). Then add those results: 15+15=30.