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Social Golfer Problem

Twenty golfers wish to play in foursomes for 5 days. Is it possible for each golfer to play no more than once with any other golfer? The answer is yes, and the following table gives a solution.

MonABCDEFGHIJKLMNOPQRST
TueAEIMBJOQCHNTDGLSFKPR
WedAGKOBIPTCFMSDHJRELNQ
ThuAHLPBKNSCEORDFIQGJMT
FriAFJNBLMRCGPQDEKTHIOS

Event organizers for bowling, golf, bridge, or tennis frequently tackle problems of this sort, unaware of the problem complexity. In general, it is an unsolved problem. A table of known results is maintained by Harvey.

See also

Kirkman's Schoolgirl Problem, Steiner Triple System

This entry contributed by Ed Pegg, Jr. (author's link)

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References

Colbourn, C. J. and Dinitz, J. H. (Eds.). "Golf Designs." §7.7 in CRC Handbook of Combinatorial Designs. Boca Raton, FL: CRC Press, pp. 570-571, 1996.Harvey, W. "The Social Golfer Problem." http://www.icparc.ic.ac.uk/~wh/golf/.Pegg, E. "Social Golfer Problem." http://demonstrations.wolfram.com/SocialGolferProblem/.

Subjects

Mathematics:Discrete Mathematics:Graph Theory:Social Network Theory

Entry

Cite this as:

Pegg, Ed Jr. "Social Golfer Problem." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/SocialGolferProblem.html

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