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Solution

The SGP is the Steiner quadruple system S(2,4,32) because 32 golfers are divided into groups of 4 and both the group and week assignments of any 2 golfers can be uniquely identified.

There are many approaches to solving the SGP.

Radix

Variables in the general case of the SGP can be redefined as $n=s^{k}$ golfers who play in $g=s^{k-1}$ groups of $s$ golfers for any number $k$. The maximum number of weeks that these golfers can play without regrouping any two golfers is ${\tfrac {k^{n}-1}{k-1}}$. The radix approach assigns golfers into groups based on the addition of numbers in base $k$.

Applications

Working in groups is encouraged in classrooms because it fosters active learning and development of critical-thinking and communication skills. The SGP has been used to assign students into groups in undergraduate chemistry classes and breakout rooms in online meeting software to maximize student interaction and socialization.

Social Golfer Problem