Bowling Tournament Schedule

[Nelson]

Hi All,

First post! Hopefully this doesn't cover a topic already covered - sorry if it does and a pointer to the relevant post would be much appreciated.

So, I'm organising a round-robin bowling tournament for 12 teams, using 12 lanes. The following constraints need to be obeyed:

• As much as possible, each team needs to not play on each lane more than once (i.e. it needs to be balanced). This should leave each team playing on 11 of the 12 lanes throughout the event.
• No team can play on the same pair of lanes in two consecutive games.

If only (1) is necessary, then any of the generated schedules in the Ian's excel sheet would be fine. But in many of these (or at least all of the ones I've tried) condition 2 is not obeyed.

So, my questions are:

1) Is it even possible to have a balanced schedule (as in the Excel file) without at least one team staying on the same pair for consecutive games?
2) Do any of the in-built schedules in the Excel sheet do this - is there a magic number?
3) If yes then no for the above, does anyone know how to generate such a schedule?

Many Thanks,

Nelson

[Ian Wakeling]

Hi Nelson,

I think this is the same problem that you can find here, except that lane pairs 7 to 12 should be re-labelled 1 to 6.  If you follow the schedules link in the other thread,  you will find some other partitioned balanced tournament designs that also satisfy your second constraint.  Generating these schedules is not so easy, but there are examples here for 10, 12,14, 16 & 20 teams, which covers all the ones that are known to exist when the number of teams is small.  Most teams play twice on any one pair of lanes, and the schedules should be arranged so that each plays once on the left and once on the right, so you could use this property to make sure that the teams never play on the same lane twice.

Hope that helps,  

Ian.