Glove Problem
Let there be 
doctors and 
patients, and let all 
possible combinations of examinations of patients bydoctors take place. Then what is the minimum number of surgical gloves needed 
so that no doctor must wear a glovecontaminated by a patient and no patient is exposed to a glove worn by another doctor? In this problem, the gloves can beturned 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 
isstraightforward since two gloves have atotal 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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