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 (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
The case
is straightforward since two gloves have a total of four surfaces, which is the number
needed for
examinations. With doctors AB, patients ab, and gloves 12, a solution is A12a, A1b,
B2a, B21b.
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 (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
![g(m,n)={2 m=n=2; 1/2(m+1) n=1, m=2k+1; [1/2(m)+2/3n] otherwise,](/images/equations/GloveProblem/NumberedEquation1.svg)
![[x]](/images/equations/GloveProblem/Inline5.svg)
is the ceiling function (Vardi 1991).
is straightforward since two gloves have a total of four surfaces, which is the number
needed for 
examinations. With doctors AB, patients ab, and gloves 12, a solution is A12a, A1b,
B2a, B21b.
