Here is a real-world problem (from the new professional football league):
Design a schedule for a 10-week season involving 8 teams playing one game a week, on Sunday. The teams are divided into two divisions, east and west.
- Each team plays the teams in its division twice, home and away.
- Each team plays the teams in the other division once.
- Each team plays 5 home games and 5 away games.
- No team ever has 3 home games in a row, or 3 away games in a row.Source: J. Dinitz and D. Froncek, U of Vermont (Dinitz was hired as a consultant by the XFL to design their schedule).
© Copyright 2001 Stan Wagon. Reproduced with permission.