Hi Gerry,

If you are one of the golfers then on each round you play with 3 other golfers. Thus in the 4 rounds you play with at most $3 \times 4 = 12$ other golfers. Hence in the 4 rounds you can't play with each of the 15 others in your group.

If you have 5 rounds you can achieve what you want. For 4 rounds take the schedule given and delete one of the days. That's the best you can do.

Harley