The instructions from Rutgers are to take from 12 to 15 samples from a single putting green. I like to check Penn State recommendations too—their websites are a wealth of reference materials. A good starting point is the Professional Turfgrass Management page with its long list of documents. My favorite from that page is Turfgrass Fertilization: A Basic Guide for Professional Turfgrass Managers.
On the soil sampling instructions page, the instructions for turf soils are:
“Using a soil sampling tube, auger or trowel, and a clean pail, obtain thin slices or borings of soil from 12 or more locations.”
I’m not sure where the 12 comes from, but Penn State recommends a minimum of 12 subsamples be put together as a composite sample for an area, and so does Rutgers. This seems to be the standard recommendation.