Let there be m doctors and n<=m patients, and let all m n possible combinations of examinations of patients by doctors take place. Then what is the minimum number of surgical gloves needed G(m, n) so that no doctor must wear a glove contaminated by a patient and no patient is exposed to a glove worn by another doctor (where it is assumed that each doctor wears a glove on a single hand only)? 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
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