A golfing variation.......

[BTM]

I am planning a golf trip for mid-June, and am struggling to ensure the best possible mix of players, ensuring everyone plays with everyone else at least once.

We are playing 4 rounds, and what makes it particularly challenging is that we have 8 golfers for Rounds 1 and 2, but only 7 for Rounds 3 and 4. If it was 7 or 8 golfers for all 4 days that would be a bit more straightforward, but the split appears to add considerable difficulty. I tried this:

R1      (8 1 7 6)  (5 2 3 4)
R2      (8 2 4 3)  (6 1 7 5)
R3      (2 1 3)  (6 5 2 7)
R4      (5 2 7)  (1 3 6 4)

with golfer #8 playing just the first two rounds. I recognise someone won't get to play with #8 (and in my example above that's #5) but I still have some players playing together 3 times, and other not at all!

Before I pull out what's left of my hair, I'd be most grateful for any assistance anyone can offer.

Many thanks - Nick  

[Ian Wakeling]

Nick,

There is not really any problem regarding golfer #8 who drops out, as we can design a full schedule and then at the end remove player 8 from two of the rounds.

It is possible to avoid having some pairs play together 3 times, and it is also possible to avoid having some pairs never meet,  but critically it is impossible to have both at the same time, I guess this is what you were looking for so I worry about your hair!

In my view the best solution is this one here.  Each player has someone they don't play with, but they play with the other six opponents exactly twice each.

Alternatively play something like this:

(1 2 7 8)  (3 4 5 6)
(1 2 5 6)  (3 4 7 8)
(1 2 3 4)  (5 6 7 8)
(1 3 5 7)  (2 4 6 8)

Note that (1 2) (3 4) (5 6) and (7 8) all play together 3 times.

Ian.

[BTM]

That's great - many thanks Ian.

Nick