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# The Glove Shortage

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A disaster has just occured and hospital has to operate on a number of patients and they are so busy that all doctors have to assist with all operations. Now, all patients may be suffering from some contagious disease, and all doctors may have picked up some contagious diseases in the hospital. In order to prevent the spread of disease, each doctor must wear operating gloves, but in order to minimize cost, he can reuse gloves under the conditions that

• Each doctor either uses a clean glove surface, or a surface that only he has come in contact with.
• Each patient is operated on by a glove with a clean outside surface or one that only he has been exposed to.
For the following values of m doctors and n patients, what is the minimum number of gloves needed?
1. m = n = 2.
2. m = 3, n = 1.
3. m = n = 6.
You are allowed to
• Nest gloves (note that nesting a clean surface in an exposed surface will lead to contamination).
• Turn gloves inside out.

© Copyright 1996 Stan Wagon. Reproduced with permission.

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2 October 1998