Terry,

I wrote a program to try to find the best answer. So far it has been running for about 5 days and has checked about 200 million of the 20 billion or so possibilities. Holding my breath waiting for it to complete sounds like a bad idea. It will probably take over a month, assuming my computer does not crash.

Here is something imperfect that you could try. There is a schedule for 9 golfers (3 threesomes) in which every pair plays together exactly once over four rounds. That should be available in the archives. What you can do is add the tenth player to one of the three group on each of the four days so that his schedule is as balanced as possible. Every other pair will be together exactly once; only pairs involving the tenth person will be "unbalanced".

--Victoria