rebrobindoesmath:

In mathematics, the Glove Problem is an optimization problem
in which the number of gloves needed for doctors to examine patients is
minimized. 

Here’s the basic setup: we have m
doctors and n patients. Each doctor
needs to examine each patient and every patient needs to be examined by every
doctor. Basically, we need to have every possible pair between doctors and
patients. To avoid contamination, the doctors must wear gloves such that each
side (we have two: inside and outside) of the glove only ever touches one
person. More than one glove can be worn at one time and gloves can be reused as
many times as needed, provided that we don’t have cross contamination.

What is the minimum number of gloves, g(m,n), required for m doctors
and n patients?

If we have just 1 doctor, we simply need one glove for every
patient, or n gloves. Similarly, if
we have just 1 patient, we need one glove for every doctor, or m gloves. Additionally, one doctor and
one patient gives g(1,1) = 1.

So we really just need to consider when we have 2 or more
doctors and 2 or more patients.

We expect the answer to be mn, since we have m doctors
and n patients, but we’re not really
utilizing a clever part of the problem: the gloves have two sides.

Here’s the strategy that will give us the minimum number of
gloves:

The first doctor wears n
gloves all simultaneously. They visit each patient in a row and remove the top
glove after examination, leaving it with the patient.

The second through (m-1)
doctor all wear one glove and as they cycle through the patients, they each put
the glove left by the first doctor over
the glove they’re wearing already and then remove it once the examination is over. We
can see still that each side of every glove has only ever touched one person.

The last doctor visits one patient and puts on the glove
left by the previous doctors and performs the examination. They move to the
next patient and put the glove left by the previous doctors over the glove they’re
currently wearing and then perform the examination. This continues on and on
until the doctor is wearing n gloves
and has examined all n patients.

How many gloves is this?

The first doctor wears n
gloves.

The second through (m-1)
doctors each wear one glove, which gives m-2
gloves.

The last doctor just uses already existing gloves and does
not use any new gloves.

So the final total is n+m-2 gloves.

While this minimizes the number of gloves and the cost of
the gloves, this is not particularly easy to execute. Have you ever tried to
take a latex glove off and have it not go inside out?? It’s pretty difficult.
Additionally, the image of the last doctor potentially putting on, like, 100
dirty gloves is a pretty humorous image and I can only imagine the struggle of putting
on that last glove.

Anyway, thanks for reading! 

I hope all is well and stay
positive! 🙂

PS: This problem is also called the condom problem, where instead of gloves, it’s condoms, and, well, I wouldn’t recommend doing that. 

[Source: Wikipedia]

dannyaviclan:

user: tittie

tumblr: 

STOP! You violated the law. Pay the court a fine or serve your sentence. Your stolen goods are now forfeit.

the-real-numbers:

@staff I’ll fight verizon for you if you don’t have the spine

tristikovbirds:

occasionallybirds:

occasionallybirds:

Great.  The bird photos I posted today were flagged as “sensitive.”  A red-eyed vireo.  Is this how the purge is going to go?

…And a quick scroll though my blog shows that Yellow-bellied Sapsuckers and Spotted Towhees also qualify as adult content

>mfw

thighschool:

powerarmor:

this icon

the chanel boots? yeah i am

miseducatedmelanicmuse: