# can 17 teams play 14 games each ?

• Nov 5th 2009, 01:29 PM
aturetsky
can 17 teams play 14 games each ?
My neighbor runs a basketball league and asked me (a computer programmer) to generate a list of match ups for him. I readily accepted, but it's turning out harder than I thought.

Is it really possible to have 17 teams each play 14 games such that they don't play each other twice?

I am beginning to suspect that it's not possible - for instance, I've proven by trial and error that you can't get 5 teams to play 3 games.

Is there a general formula I can use to determine whether a given number of teams can play a given number of games w/o playing each other twice?
• Nov 6th 2009, 07:24 AM
InvisibleMan
How about brute force to help us in this problem?

Pick one team from 17 teams, and then decide arbitrarilty their 14 oppnenets, let's mark the teams as 1-17.
then: 1 will face 2-15.
2 will face 1 and 3-15.
3 will face 1 and 2 and 4-15.
4 will face 1 and 2 and 3 and 5-15.
5 will face 1,2,3,4 and 6-15.
6 will face 1,2,3,4,5 and 7-15
7 will face 1,2,3,4,5,6 and 8-15.
8 will face 1,2,3,4,5,6,7 and 9-15.
9 will face 1-8 and 10-15.
10 will face 1-9 and 11-15
11 will face 1-10 and 12-15
12 will face 1-11 and 13-15
13 will face 1-12 and 14-15
14 will face 1-13 and 15.
15 will face 1-14.
Now for 16 and 17 you have the freedom to choose which they should play against, because we have 15 teams to choose from.

I might have some errors as I haven't checked it thoroughly.