Best host

By John Toczek

Hosting a dinner party requires several skills to pull off a successful evening. One of your duties, aside from preparing dinner and selecting the drinks, is to make sure your guests enjoy themselves.

Figure 1 shows a dinner table with six seats for your guests. Some guests, however, do not get along with each other. If two guests who do not get along are seated next to each other, it will create conflict at dinner. As host, you must arrange the guests in a seating order that minimizes conflict.

Andrew will only sit next to Dave and Frank; Betty will only sit next to Cara and Erica; Cara will only sit next to Betty and Frank; Dave will only sit next to Andrew and Erica; Erica will only sit next to Betty and Dave; Frank will only sit next to Andrew and Cara. In the example seating arrangement above, there are three conflicts (Andrew and Betty, Cara and Dave, Erica and Frank).


Figure 1: How can these six guests get along?


What seating arrangement will minimize the conflict at dinner?

Send your answer to by April 15. The winner, chosen randomly from correct answers, will receive an “O.R. The Science of Better” T-shirt. Congratulations to Dan Cullen for correctly solving October’s Home Improvement PuzzlOR. Past questions can be found at

John Toczek is the senior decision support analyst for ARAMARK Corporation in the Global Risk Management group. He earned a bachelor’s degree in chemical engineering at Drexel University (1996) and a master’s degree in operations research from Virginia Commonwealth University (2005).