SECOND ANSWERS Dr. Xenophon wears both pairs of gloves. Sides 1A and 2B may become contaminated, while IB and 2A remain sterile. Dr. Ypsilanti wears the second pair, with sterile sides 2A against his hands. Dr. Zeno turns the first pair inside out and then puts them on with sterile sides IB against his hands. Then he puts on the second pair, with sides 2A over sides 1A and sides 2B outermost. Because only sides 2B touch Ms. Hooker in all three operations, she runs no risk of catching the Barsoomian flu from any of the surgeons.
POSTSCRIPT
As far as I know, this was the first publication of an amusing problem that had been circulating privately among mathematicians for many years. The original problem, of unknown origin, concerned three male mathematicians who were attending a conference on combinatorics. To gether they took an evening off to visit a local prostitute. They were uncertain of one another’s health, as well as the health of the lady. Between them they had only two prophylactics. How could the two devices be used for their protection? The problem was soon extended, also by an unknown person, to include protection for the lady. Eventually it was generalized to n men and m ladies who paired off in all possible male-female ways. What is the minimum number of devices that provide safety for everyone? Whether this general problem has been solved or not, I do not know. In 1977 a partial solution was found by Richard Lipton, a computer scientist at Yale University, at the same time, independently, by two Hungarian mathematicians, A. Hajnal and L. Lovasz. Hajnal and Lovasz titled their paper, “An Algorithm to Prevent the Propagation of Certain Diseases at Minimal Cost.” The abstract of their paper follows:
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