Math CentralQuandaries & Queries


Question from scott:

i am looking for a schedule for 32 golfers to play 6 rounds and never play with the same person twice.
I made one for 28 golfers but i am struggling with 32.


Here is a 10-day schedule taken from The first 6 days will work for you.


32 golfers playing in foursomes for 10 days. This problem has been on the Social Golfer Problem page, in a 1998 sci.ops-research usenet posting, in, and in Google answers. Lots of wrong answers, unfortunately. The problem was first solved by Hao Shen in 1996, and independently solved by Charles Colbourn in 1999. In 2004, Alejandro Aguado came across the problem, and realized 4-RGDD (Resolvable Group Divisible Design) would solve the problem, and used Coulbourn's paper to produce "A 10 Days Solution to the Social Golfer Problem." In this solution, couples Aa-Oo all play once with everyone but their spouse.

Day0 ABCD EFGH IJKL MNPO abcd efgh ijkl mnop
Day1 AEIm BgcH DFKp kPdf Maei ChbG jNoL lJnO
Day2 Alof Bhkm DNGi FaLO MbHK CPeJ Ejcp gIdn
Day3 AciL BjdK DkbJ FgoP fGOp CIla EhMn NeHm
Day4 AgNK BElP DIoH hdiO beLp Cjfm FMcJ kaGn
Day5 AhJp BFin DcmO INbf leGK CMod EgkL jPaH
Day6 AFde BoGJ DEaf hlNc PiKm CHLn gjbO IkMp
Day7 APbn BNap DglM koce fHiJ CEKO FhIj dGLm
Day8 AjMG BIeO DhPL gaJm cfKn CFkN Eobi ldHp
Day9 AkHO BMfL Djen Flbm IPcG Cgip ENdJ hoaK

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