Dirty math post by Tanya Khovanova

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Ya… so…
Tanya Khovanova has a dirty post on her math blog:

It has to do with what she calls the condom puzzle. Basically, it’s a variation of the glove problem:

Suppose there are “m” doctors and “n” patients (with “n<=m”). There are “mn” combination’s of examinations that pair doctors/patients. How many surgical gloves are needed so that no doctor wears a glove contaminated by a patient, and no patient is exposed to a glove worn by another doctor?

Of course “mn” is an upper bound, but the minimum number is much smaller (can you see why?).