Let there be doctors and patients, and let all possible combinations of examinations of patients by
doctors take place. Then what is the minimum number of surgical gloves needed so that no doctor must wear a glove
contaminated by a patient and no patient is exposed to a glove worn by another doctor? In this problem, the gloves can be
turned inside out and even placed on top of one another if necessary, but no ``decontamination'' of gloves is permitted.
The optimal solution is

where is the Ceiling Function (Vardi 1991). The case is straightforward since two gloves have a total of four surfaces, which is the number needed for examinations.

**References**

Gardner, M. *Aha! Insight.* New York: Scientific American, 1978.

Gardner, M. *Science Fiction Puzzle Tales.* New York: Crown, pp. 5, 67, and 104-150, 1981.

Hajnal, A. and Lovász, L. ``An Algorithm to Prevent the Propagation of Certain Diseases at Minimum Cost.''
§10.1 in *Interfaces Between Computer Science and Operations Research* (Ed. J. K. Lenstra, A. H. G. Rinnooy Kan,
and P. van Emde Boas). Amsterdam: Matematisch Centrum, 1978.

Orlitzky, A. and Shepp, L. ``On Curbing Virus Propagation.'' Exercise 10.2 in Technical Memo. Bell Labs, 1989.

Vardi, I. ``The Condom Problem.'' Ch. 10 in *Computational Recreations in Mathematica.*
Redwood City, CA: Addison-Wesley, p. 203-222, 1991.

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1999-05-25