Terry,

it depends on what you mean by "a different foursome". I'll take it to mean that every pair of players plays together exactly once. There are 36x35/2 = 630 different pairs of players from among 36. Each foursome accounts for 6 of them, so 9 foursomes (one week) accounts for 54 of them. Since 630 is not divisible by 54, the arrangement it isn't possible. It takes 12 weeks for each pair to play together at least once. It might be possible to have most pairs play together once and some play together twice over 12 weeks. That's the minimum number of weeks required for that to happen. I don't know if can be arranged though.

--Victoria