THE PUZZLOR
The matchmaker
By John Toczek
The matchmaker was an honored profession in past cultures, serving the valuable purpose of pairing off men and women in hopes of a long and successful relationship. The matchmaker would carefully consider the characteristics of each partner to determine which pairs would be compatible.
Figure 1 shows six men and six women each with varying hair color and eye color. A man or woman will only accept a partner that has at least one of these traits in common. For example, Man A and Women 5 would make a matching pair because they have at least one trait in common (same hair color). However, Man A and Women 1 would not make a matching pair because they do not have any traits in common.
Figure 1: Matchmaker, matchmaker make me a match.
Question:
What pairings of men and women allow for everyone to have a partner with at least one trait in common? (There are several correct answers.)?
Send your answer to puzzlor@gmail.com by Aug. 15. The winner, chosen randomly from correct answers, will receive an “O.R. The Science of Better” T-shirt. Congratulations to Scott Wiederhold for correctly solving February’s “Best Host” PuzzlOR. Past questions can be found at puzzlor.com.
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).
