Mathematician Alan Hoffman is responsible for many landmark achievements in optimization, combinatorics, and linear algebra. Since 1961, he has worked in the Mathematical Sciences department at the IBM Research Center in Yorktown Heights, New York. Dr. Irv Lustig met with him there to talk about his early work at the National Bureau of Standards, and his contributions to the growth of optimization.
When asked to be as nontechnical as possible, Hoffman replied, "There's only one piece of mathematics that I've done where I can explain the problem fully. It has to do with scheduling a round-robin mixed doubles tennis tournament for a number of couples.
You want to arrange matches so that husband and wife never play together and never oppose each other. Apart from that restriction, each player meets each player of the same sex once; and each player plays with each player of the opposite sex (other
than the spouse) once as partners and once as opponents. My colleagues and I showed that you could do this for any number of couples except two, three or six. This is the only problem I've ever solved that I could explain to a layman completely."
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